publications | Manuel Laínz Valcázar

2026

Symplectic Approach to Global Stability

Verónica Errasti Díez, Jordi Gaset Rifá, and Manuel Lainz Valcázar

In Geometric Science of Information, 2026

Abs DOI arXiv Bib

We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum map is everywhere regular. Our results take root in the recently proposed notion of a confining function and are motivated by ghost-ridden systems, for whom we put forward the first geometric definition.
@inproceedings{errastidiezSymplecticApproachGlobal2026, title = {Symplectic {{Approach}} to {{Global Stability}}}, author = {Errasti D{\'i}ez, Ver{\'o}nica and Gaset Rif{\'a}, Jordi and Lainz Valc{\'a}zar, Manuel}, editor = {Nielsen, Frank and Barbaresco, Fr{\'e}d{\'e}ric}, year = {2026}, booktitle = {Geometric {{Science}} of {{Information}}}, pages = {320--327}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {978-3-032-03924-8}, doi = {10.1007/978-3-032-03924-8_33}, }

2025

Liouville–Arnold Theorem for Homogeneous Symplectic and Contact Hamiltonian Systems

Leonardo Colombo, Manuel de León, Manuel Lainz, and 1 more author

Geometric Mechanics, Sep 2025

Abs DOI arXiv Bib

A Hamiltonian system is completely integrable (in the sense of Liouville) if there exist as many independent integrals of motion in involution as the dimension of the configuration space. Under certain regularity conditions, Liouville–Arnold theorem states that the invariant geometric structure associated with Liouville integrability is a fibration by Lagrangian tori (or, more generally, Abelian Lie groups), on which the motion is linear. In this paper, a Liouville–Arnold theorem for contact Hamiltonian systems is proven. More specifically, it is shown that, given a ( 2 n + 1 ) (2n+1) -dimensional completely integrable contact system, one can construct a foliation by ( n + 1 ) (n+1) -dimensional Abelian Lie groups and induce action-angle coordinates in which the equations of motion are linearized. One important novelty with respect to previous attempts is that the foliation consists of ( n + 1 ) (n+1) -dimensional coisotropic submanifolds given by the preimages of rays by the functions in involution. In order to prove the theorem, we first develop a version of Liouville–Arnold theorem for homogeneous functions on exact symplectic manifolds (which is of independent interest), and then apply the symplectization to obtain the contact case.
@article{colomboLiouvilleArnoldTheorem2025, title = {Liouville--{{Arnold}} Theorem for Homogeneous Symplectic and Contact {{Hamiltonian}} Systems}, author = {Colombo, Leonardo and {de Le{\'o}n}, Manuel and Lainz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier}, year = {2025}, month = sep, journal = {Geometric Mechanics}, volume = {02}, number = {03}, pages = {275--307}, publisher = {World Scientific Publishing Co.}, issn = {2972-4589}, doi = {10.1142/S2972458925400039}, }

2024

The Herglotz Variational Principle for Dissipative Field Theories

Jordi Gaset, Manuel Lainz, Arnau Mas, and 1 more author

Geometric Mechanics, Jun 2024

Abs DOI arXiv Bib

In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when studying contact Hamiltonian systems can also be obtained via the Herglotz variational principle. The contact Lagrangian and Hamiltonian formalisms for mechanical systems has also been generalized to field theories. The main goal of this paper is to develop a generalization of the Herglotz variational principle for first-order and higher-order field theories. In order to illustrate this, we study three examples: the damped vibrating string, the Korteweg–de Vries equation, and an academic example showing that the non-holonomic and the vakonomic variational principles are not fully equivalent.
@article{gasetHerglotzVariationalPrinciple2024, title = {The {{Herglotz}} Variational Principle for Dissipative Field Theories}, author = {Gaset, Jordi and Lainz, Manuel and Mas, Arnau and Rivas, Xavier}, year = {2024}, month = jun, journal = {Geometric Mechanics}, volume = {01}, number = {02}, pages = {153--178}, publisher = {World Scientific Publishing Co.}, issn = {2972-4589}, doi = {10.1142/S2972458924500060}, }

A New Perspective on Nonholonomic Brackets and Hamilton-Jacobi Theory

Manuel de León, Manuel Laínz, Asier López-Gordón, and 1 more author

Journal of Geometry and Physics, Apr 2024

DOI arXiv Bib

@article{lopezgordonNewPerspectiveNonholonomic2024,
  title = {A New Perspective on Nonholonomic Brackets and {{Hamilton-Jacobi}} Theory},
  author = {{de Le\'on}, Manuel and La\'inz, Manuel and {L\'opez-Gord\'on}, Asier and {Marrero}, Juan Carlos},
  year = {2024},
  month = apr,
  journal = {Journal of Geometry and Physics},
  volume = {198},
  pages = {105116},
  issn = {0393-0440},
  doi = {10.1016/j.geomphys.2024.105116},
}

2023

Hamilton–Jacobi Theory and Integrability for Autonomous and Non-Autonomous Contact Systems

Manuel de León, Manuel Lainz, Asier López-Gordón, and 1 more author

Journal of Geometry and Physics, May 2023

Abs DOI arXiv Bib

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton–Jacobi theory for these systems following two approaches, obtaining two different Hamilton–Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not. In order to illustrate the theory developed in this paper, we study three examples: the free particle with a linear external force, the freely falling particle with linear dissipation and the damped and forced harmonic oscillator.
@article{deleonHamiltonJacobiTheory2023, title = {Hamilton--{{Jacobi}} Theory and Integrability for Autonomous and Non-Autonomous Contact Systems}, author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier and Rivas, Xavier}, year = {2023}, month = may, journal = {Journal of Geometry and Physics}, volume = {187}, pages = {104787}, issn = {0393-0440}, doi = {10.1016/j.geomphys.2023.104787}, }
Nonholonomic Brackets: Eden Revisited

Manuel de León, Manuel Lainz, Asier López-Gordón, and 1 more author

In Geometric Science of Information, 2023

Abs DOI arXiv Bib

The nonholonomic dynamics can be described by the so-called nonholonomic bracket in the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in this case, of the canonical bracket in the cotangent bundle of the configuration manifold. This bracket was defined in [2, 10], although there was already some particular and less direct definition. On the other hand, another bracket, also called noholonomic, was defined using the description of the problem in terms of skew-symmetric algebroids. Recently, reviewing two older papers by R. J. Eden, we have defined a new bracket which we call Eden bracket. In the present paper, we prove that these three brackets coincide. Moreover, the description of the nonholonomic bracket à la Eden has allowed us to make important advances in the study of Hamilton-Jacobi theory and the quantization of nonholonomic systems.
@inproceedings{deleonNonholonomicBracketsEden2023, title = {Nonholonomic {{Brackets}}: {{Eden Revisited}}}, author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier and Marrero, Juan Carlos}, editor = {Nielsen, Frank and Barbaresco, Fr{\'e}d{\'e}ric}, year = {2023}, booktitle = {Geometric {{Science}} of {{Information}}}, series = {Lecture {{Notes}} in {{Computer Science}}}, pages = {105--112}, publisher = {Springer Nature Switzerland}, address = {Cham}, isbn = {978-3-031-38299-4}, doi = {10.1007/978-3-031-38299-4_12}, }

2022

Geometric Hamilton–Jacobi Theory for Systems with External Forces

Manuel de León, Manuel Lainz, and Asier López-Gordón

Journal of Mathematical Physics, Feb 2022

DOI arXiv Bib

@article{deleonGeometricHamiltonJacobi2022,
  title = {Geometric {{Hamilton}}--{{Jacobi}} Theory for Systems with External Forces},
  author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier},
  year = {2022},
  month = feb,
  journal = {Journal of Mathematical Physics},
  volume = {63},
  number = {2},
  pages = {022901},
  issn = {0022-2488, 1089-7658},
  doi = {10.1063/5.0073214},
}

Inverse Problem and Equivalent Contact Systems

Manuel de León, Jordi Gaset, and Manuel Lainz

Journal of Geometry and Physics, Mar 2022

DOI arXiv Bib

@article{deleonInverseProblemEquivalent2022,
  title = {Inverse Problem and Equivalent Contact Systems},
  author = {{de Le{\'o}n}, Manuel and Gaset, Jordi and Lainz, Manuel},
  year = {2022},
  month = mar,
  journal = {Journal of Geometry and Physics},
  volume = {176},
  pages = {104500},
  issn = {03930440},
  doi = {10.1016/j.geomphys.2022.104500},
}

Optimal Control, Contact Dynamics and Herglotz Variational Problem

Manuel de León, Manuel Lainz, and Miguel C. Muñoz-Lecanda

Journal of Nonlinear Science, Nov 2022

Abs DOI arXiv Bib

In this paper, we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin maximum principle. As an important result, among others, we develop a contact Pontryagin maximum principle that permits to deal with optimal control problems with dissipation. We also consider the Herglotz optimal control problem, which is simultaneously a generalization of the Herglotz variational principle and an optimal control problem. An application to the study of a thermodynamic system is provided.
@article{deleonOptimalControlContact2022, title = {Optimal {{Control}}, {{Contact Dynamics}} and {{Herglotz Variational Problem}}}, author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {Mu{\~n}oz-Lecanda}, Miguel C.}, year = {2022}, month = nov, journal = {Journal of Nonlinear Science}, volume = {33}, number = {1}, pages = {9}, issn = {1432-1467}, doi = {10.1007/s00332-022-09861-2}, }
Reviewing the Geometric Hamilton-Jacobi Theory Concerning Jacobi and Leibniz Identities

Oğul Esen, Manuel de Leon, Manuel Lainz Valcázar, and 2 more authors

Journal of Physics A: Mathematical and Theoretical, Sep 2022

Abs DOI arXiv Bib

Abstract In this survey, we review the classical Hamilton–Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton-Jacobi equation for different geometric structures attending to one particular characterization: whether they fulfill the Jacobi and Leibniz identities simultaneously, or if at least they satisfy one of them. In this regard, we review the case of time-dependent (\t\-dependent in the sequel) and dissipative physical systems as systems that fulfill the Jacobi identity but not the Leibnitz identity. Furthermore, we review the contact-evolution Hamilton-Jacobi theory as a split off the regular contact geometry, and that actually satisfies the Leibniz rule instead of Jacobi. Furthermore, we include a novel result, which is the Hamilton-Jacobi equation for conformal Hamiltonian vector fields as a generalization of the well-known Hamilton-Jacobi on a symplectic manifold, that is retrieved in the case of a zero conformal factor. The interest of a geometric Hamilton–Jacobi equation is the primordial observation that if a Hamiltonian vector field \X_H can be projected into a configuration manifold by means of a \1\-form \dW then the integral curves of the projected vector field \X_\textbraceleft H\textbraceright^\textbraceleft dW\textbraceright can be transformed into integral curves of \X_H provided that \W is a solution of the Hamilton-Jacobi equation. Geometrically, the solution of the Hamilton-Jacobi equation plays the role of a Lagrangian submanifold of a certain bundle. Exploiting these features in different geometric scenarios we propose a geometric theory for multiple physical systems depending on the fundamental identities that their dynamic satisfies. Different examples are pictured to reflect the results provided, being all of them new, except for one that is reassessment of a previously considered example.
@article{esenReviewingGeometricHamiltonJacobi2022, title = {Reviewing the Geometric {{Hamilton-Jacobi}} Theory Concerning {{Jacobi}} and {{Leibniz}} Identities}, author = {Esen, O{\u g}ul and {de Leon}, Manuel and Lainz Valc{\'a}zar, Manuel and Sard{\'o}n, Cristina and Zaj{\k a}c, Marcin}, year = {2022}, month = sep, journal = {Journal of Physics A: Mathematical and Theoretical}, issn = {1751-8113, 1751-8121}, doi = {10.1088/1751-8121/ac901a}, }

Discrete Hamilton-Jacobi Theory for Systems with External Forces

Manuel de León, Manuel Laínz, and Asier López-Gordón

Journal of Physics A: Mathematical and Theoretical, May 2022

DOI arXiv Bib

@article{deleonDiscreteHamiltonJacobi2022,
  title = {Discrete {{Hamilton-Jacobi}} Theory for Systems with External Forces},
  author = {{de Le{\'o}n}, Manuel and La{\'i}nz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier},
  year = {2022},
  month = may,
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {55},
  number = {20},
  pages = {205201},
  doi = {10.1088/1751-8121/ac6240},
}

2021

On the Geometry of Discrete Contact Mechanics

Alexandre Anahory Simoes, David Martín de Diego, Manuel Lainz, and 1 more author

Journal of Nonlinear Science, Apr 2021

Abs DOI arXiv Bib

In this paper, we continue the construction of variational integrators adapted to contact geometry started in Vermeeren et al. (J Phys A 52(44):445206, 2019), in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed.
@article{anahorysimoesGeometryDiscreteContact2021, title = {On the {{Geometry}} of {{Discrete Contact Mechanics}}}, author = {Anahory Simoes, Alexandre and {Mart{\'i}n de Diego}, David and Lainz, Manuel and {de Le{\'o}n}, Manuel}, year = {2021}, month = apr, journal = {Journal of Nonlinear Science}, volume = {31}, number = {3}, pages = {53}, issn = {1432-1467}, doi = {10.1007/s00332-021-09708-2}, }
The Geometry of Some Thermodynamic Systems

Alexandre Anahory Simoes, David Martín de Diego, Manuel Lainz, and 1 more author

In Geometric Structures of Statistical Physics, Information Geometry, and Learning, 2021

Abs DOI arXiv Bib

In this article, we continue the program started in [2] of exploring an important class of thermodynamic systems from a geometric point of view. The contents of this paper and the one already published in [2] provide a geometrical formulation, which tries to shed more light on the properties of thermodynamic systems without claiming to be a definitive theory. In order to model the time evolution of systems verifying the two laws of thermodynamics, we show that the notion of evolution vector field is adequate to appropriately describe such systems. Our formulation naturally arises from the introduction of a skew-symmetric bracket to which numerical methods based on discrete gradients fit nicely. Moreover, we study the corresponding Lagrangian and Hamiltonian formalism, discussing the fundamental principles from which the equations are derived. An important class of systems that is naturally covered by our formalism are composed thermodynamic systems, which are described by at least two thermal variables and exchange heat between its components.
@inproceedings{anahorysimoesGeometryThermodynamicSystems2021, title = {The {{Geometry}} of {{Some Thermodynamic Systems}}}, author = {Anahory Simoes, Alexandre and {Mart{\'i}n de Diego}, David and Lainz, Manuel and {de Le{\'o}n}, Manuel}, editor = {Barbaresco, Fr{\'e}d{\'e}ric and Nielsen, Frank}, year = {2021}, booktitle = {Geometric {{Structures}} of {{Statistical Physics}}, {{Information Geometry}}, and {{Learning}}}, series = {Springer {{Proceedings}} in {{Mathematics}} \& {{Statistics}}}, pages = {247--275}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-77957-3}, doi = {10.1007/978-3-030-77957-3_13}, }

Constrained Lagrangian Dissipative Contact Dynamics

Manuel de León, Manuel Laínz, Miguel C. Muñoz-Lecanda, and 1 more author

Journal of Mathematical Physics, Dec 2021

DOI arXiv Bib

@article{deleonConstrainedLagrangianDissipative2021,
  title = {Constrained {{Lagrangian}} Dissipative Contact Dynamics},
  author = {{de Le{\'o}n}, Manuel and La{\'i}nz, Manuel and {Mu{\~n}oz-Lecanda}, Miguel C. and {Rom{\'a}n-Roy}, Narciso},
  year = {2021},
  month = dec,
  journal = {Journal of Mathematical Physics},
  volume = {62},
  number = {12},
  pages = {122902},
  issn = {0022-2488, 1089-7658},
  doi = {10.1063/5.0071236},
}

The Hamilton–Jacobi Theory for Contact Hamiltonian Systems

Manuel de León, Manuel Lainz, and Álvaro Muñiz-Brea

Mathematics, Aug 2021

Abs DOI arXiv Bib

The aim of this paper is to develop a Hamilton–Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton–Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian function. We also analyze the corresponding formulation on the symplectification of the contact Hamiltonian system, and establish the relations between these two approaches. In the last section, some examples are discussed.
@article{deleonHamiltonJacobiTheory2021, title = {The {{Hamilton}}--{{Jacobi Theory}} for {{Contact Hamiltonian Systems}}}, author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {Mu{\~n}iz-Brea}, {\'A}lvaro}, year = {2021}, month = aug, journal = {Mathematics}, volume = {9}, number = {16}, pages = {1993}, issn = {2227-7390}, doi = {10.3390/math9161993}, }

The Herglotz Principle and Vakonomic Dynamics

Manuel de León, Manuel Lainz, and Miguel C. Muñoz-Lecanda

In Geometric Science of Information, 2021

DOI arXiv Bib

@incollection{deleonHerglotzPrincipleVakonomic2021,
  title = {The {{Herglotz Principle}} and {{Vakonomic Dynamics}}},
  author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {Mu{\~n}oz-Lecanda}, Miguel C.},
  editor = {Nielsen, Frank and Barbaresco, Fr{\'e}d{\'e}ric},
  year = {2021},
  booktitle = {Geometric {{Science}} of {{Information}}},
  volume = {12829},
  pages = {183--190},
  publisher = {Springer International Publishing},
  address = {Cham},
  isbn = {978-3-030-80208-0},
  doi = {10.1007/978-3-030-80209-7_21},
}

Higher-Order Contact Mechanics

Manuel de León, Jordi Gaset, Manuel Lainz, and 2 more authors

Annals of Physics, Feb 2021

Abs DOI arXiv Bib

We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, TkQ\texttimes R, whose geometric structures are previously introduced in order to state the Lagrangian and Hamiltonian formalisms for these kinds of systems, including their variational formulation. The variational principle, the contact forms, and the geometric dynamical equations are obtained by using those structures and generalizing the standard formulation of contact Lagrangian and Hamiltonian systems. As an alternative approach, we develop a unified description that encompasses the Lagrangian and Hamiltonian equations as well as their relationship through the Legendre map; all of them are obtained from the contact dynamical equations and the constraint algorithm that is implemented because, in this formalism, the dynamical systems are always singular. Some interesting examples are finally analysed using these geometric formulations.
@article{deleonHigherorderContactMechanics2021, title = {Higher-Order Contact Mechanics}, author = {{de Le{\'o}n}, Manuel and Gaset, Jordi and Lainz, Manuel and {Mu{\~n}oz-Lecanda}, Miguel C. and {Rom{\'a}n-Roy}, Narciso}, year = {2021}, month = feb, journal = {Annals of Physics}, volume = {425}, pages = {168396}, issn = {0003-4916}, doi = {10.1016/j.aop.2021.168396}, }

Symmetries, Constants of the Motion, and Reduction of Mechanical Systems with External Forces

Manuel de León, Manuel Lainz, and Asier López-Gordón

Journal of Mathematical Physics, Apr 2021

DOI arXiv Bib

@article{deleonSymmetriesConstantsMotion2021,
  title = {Symmetries, Constants of the Motion, and Reduction of Mechanical Systems with External Forces},
  author = {{de Le{\'o}n}, Manuel and Lainz, Manuel and {L{\'o}pez-Gord{\'o}n}, Asier},
  year = {2021},
  month = apr,
  journal = {Journal of Mathematical Physics},
  volume = {62},
  number = {4},
  pages = {042901},
  issn = {0022-2488, 1089-7658},
  doi = {10.1063/5.0045073},
}

Contact Dynamics: Legendrian and Lagrangian Submanifolds

Oğul Esen, Manuel Lainz, Manuel de León, and 1 more author

Mathematics, Jan 2021

Abs DOI arXiv Bib

We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew’s triple is constructed for evolution contact dynamics.
@article{esenContactDynamicsLegendrian2021, title = {Contact {{Dynamics}}: {{Legendrian}} and {{Lagrangian Submanifolds}}}, author = {Esen, O{\u g}ul and Lainz, Manuel and {de Le{\'o}n}, Manuel and Marrero, Juan Carlos}, year = {2021}, month = jan, journal = {Mathematics}, volume = {9}, number = {21}, pages = {2704}, publisher = {Multidisciplinary Digital Publishing Institute}, issn = {2227-7390}, doi = {10.3390/math9212704}, }

2020

Contact Geometry for Simple Thermodynamical Systems with Friction

Alexandre Anahory Simoes, Manuel de León, Manuel Lainz, and 1 more author

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Sep 2020

Abs DOI arXiv Bib

By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems.
@article{anahorysimoesContactGeometrySimple2020, title = {Contact Geometry for Simple Thermodynamical Systems with Friction}, author = {Anahory Simoes, Alexandre and {de Le{\'o}n}, Manuel and Lainz, Manuel and {Mart{\'i}n de Diego}, David}, year = {2020}, month = sep, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {476}, number = {2241}, pages = {20200244}, issn = {1364-5021, 1471-2946}, doi = {10.1098/rspa.2020.0244}, }
Contact Hamiltonian and Lagrangian Systems with Nonholonomic Constraints

Manuel de León, Víctor Manuel Jiménez, and Manuel Lainz

Journal of Geometric Mechanics, Dec 2020

Abs DOI arXiv Bib

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz’s variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.
@article{deleonContactHamiltonianLagrangian2020, title = {Contact {{Hamiltonian}} and {{Lagrangian}} Systems with Nonholonomic Constraints}, author = {{de Le{\'o}n}, Manuel and Jim{\'e}nez, V{\'i}ctor Manuel and Lainz, Manuel}, year = {2020}, month = dec, journal = {Journal of Geometric Mechanics}, issn = {1941-4889}, doi = {10.3934/jgm.2021001}, }

Infinitesimal Symmetries in Contact Hamiltonian Systems

Manuel de León and Manuel Lainz

Journal of Geometry and Physics, Jul 2020

DOI arXiv Bib

@article{deleonInfinitesimalSymmetriesContact2020,
  title = {Infinitesimal Symmetries in Contact {{Hamiltonian}} Systems},
  author = {{de Le{\'o}n}, Manuel and Lainz, Manuel},
  year = {2020},
  month = jul,
  journal = {Journal of Geometry and Physics},
  volume = {153},
  pages = {103651},
  issn = {03930440},
  doi = {10.1016/j.geomphys.2020.103651},
}

Unified Lagrangian-Hamiltonian Formalism for Contact Systems

Manuel de León, Jordi Gaset, Manuel Lainz, and 2 more authors

Fortschritte der Physik, Aug 2020

DOI arXiv Bib

@article{deleonUnifiedLagrangianHamiltonianFormalism2020,
  title = {Unified {{Lagrangian}}-{{Hamiltonian Formalism}} for {{Contact Systems}}},
  author = {{de Le{\'o}n}, Manuel and Gaset, Jordi and Lainz, Manuel and Rivas, Xavier and Rom{\'a}n-Roy, Narciso},
  year = {2020},
  month = aug,
  journal = {Fortschritte der Physik},
  volume = {68},
  number = {8},
  pages = {2000045},
  issn = {0015-8208, 1521-3978},
  doi = {10.1002/prop.202000045},
}

2019

Contact Hamiltonian Systems

Manuel de León and Manuel Lainz

Journal of Mathematical Physics, Oct 2019

Abs DOI arXiv Bib

@article{deleonContactHamiltonianSystems2019,
  title = {Contact Hamiltonian Systems},
  author = {{de Le{\'o}n}, Manuel and Lainz, Manuel},
  year = {2019},
  month = oct,
  journal = {Journal of Mathematical Physics},
  volume = {60},
  number = {10},
  pages = {102902},
  doi = {10.1063/1.5096475},
}

Singular Lagrangians and Precontact Hamiltonian Systems

Manuel de León and Manuel Lainz

International Journal of Geometric Methods in Modern Physics, Aug 2019

Abs DOI arXiv Bib

In this paper, we discuss the singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac–Bergmann algorithm). We also construct the Hamiltonian counterpart and prove the equivalence with the Lagrangian side. A Dirac–Jacobi bracket is constructed similar to the Dirac bracket.
@article{deleonSingularLagrangiansPrecontact2019, title = {Singular {{Lagrangians}} and Precontact {{Hamiltonian}} Systems}, author = {{de Le{\'o}n}, Manuel and Lainz, Manuel}, year = {2019}, month = aug, journal = {International Journal of Geometric Methods in Modern Physics}, volume = {16}, number = {10}, pages = {1950158}, issn = {0219-8878}, doi = {10.1142/S0219887819501585}, }

Plasma in a Monopole Background Does Not Have a Twisted Poisson Structure

Manuel Lainz, Cristina Sardón, and Alan Weinstein

Physical Review D, Nov 2019

DOI Bib

@article{lainzPlasmaMonopoleBackground2019,
  title = {Plasma in a Monopole Background Does Not Have a Twisted {{Poisson}} Structure},
  author = {Lainz, Manuel and Sard{\'o}n, Cristina and Weinstein, Alan},
  year = {2019},
  month = nov,
  journal = {Physical Review D},
  volume = {100},
  number = {10},
  pages = {105016},
  issn = {2470-0010, 2470-0029},
  doi = {10.1103/PhysRevD.100.105016},
}

2017

Pfaffian Correlation Functions of Planar Dimer Covers

Michael Aizenman, Manuel Lainz, and Simone Warzel

Journal of Statistical Physics, 2017

Abs DOI arXiv Bib

The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial/topological argument. These functions are then extended into a larger family of order–disorder correlation functions which are shown to exhibit Pfaffian structure throughout the bulk. Key tools involve combinatorial switching symmetries which are identified through the loop-gas representation of the double dimer model, and topological implications of planarity.
@article{aizenmanPfaffianCorrelationFunctions2017, title = {Pfaffian {{Correlation Functions}} of {{Planar Dimer Covers}}}, author = {Aizenman, Michael and Lainz, Manuel and Warzel, Simone}, year = {2017}, journal = {Journal of Statistical Physics}, volume = {166}, number = {3}, pages = {1078--1091}, issn = {1572-9613}, doi = {10.1007/s10955-016-1684-8}, }