Asier López-Gordón

Research interests

My main research interests are differential (super)geometry and its applications to mathematical physics. I am particularly interested in symplectic, Poisson, contact, Jacobi, and similar geometric structures, as well as their applications to dynamical systems.

In my doctoral dissertation, The geometry of dissipation (September 2024), I considered different geometric frameworks for modelling non-conservative dynamics, with a special emphasis on the aspects related to the symmetries and integrability of these systems. More specifically, I explored three classes of geometric frameworks modeling dissipative systems: systems with external forces, contact systems, and systems with impacts.

In a broad sense, my recent research has been mainly concerned with coordinates in which different geometric structures have a canonical form. On the one hand, I have been working on a notion of complete integrability for contact Hamiltonian dynamics. Together with L. Colombo, M. de León, and M. Lainz, we proved a Liouville-Arnold theorem for contact Hamiltonian systems, leading to action-angle coordinates in which both the contact form and the Hamiltonian dynamics have a canonical expression. On the other hand, together with J. Grabowski, we have been investigating homogeneous one-forms on graded (super)manifolds, constructing homogeneous coordinates in which the differential form has a canonical expression. Both lines of research are in fact connected, as our approach to completely integrable contact systems is based on the one-to-one correspondence between contact and homogeneous symplectic manifolds.

Profiles

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    arXiv
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    Google Scholar
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    MathSciNet MR Author Id: 1431337
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    ORCID: 0000-0002-9620-9647
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    Scopus Author Identifier: 57222113719
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    Web of Science ResearcherID: AAN-4932-2021
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    ResearchGate
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    Zotero

Publications

The publications in PDF can be downloaded by clicking on the icon .

Preprints

J. Grabowski and A. López-Gordón, “Homogeneity actions, N-manifolds, and the Frobenius theorem”, June 2026, arXiv:2606.27135 [math.DG]

Journal articles

L. Colombo and A. López-Gordón, “Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure”, Anal. Math. Phys. 16 (118), 2026, doi: 10.1007/s13324-026-01265-9

J. Grabowski and A. López-Gordón, “A Darboux classification of homogeneous Pfaffian forms on graded manifolds”, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 120 (88), 2026, doi: 10.1007/s13398-026-01885-7

J. Bajo, M. de León, and A. López-Gordón, “Geometric integrators for adiabatically closed simple thermodynamic systems”, J. Phys. A: Math. Theor., Jan. 2026, doi: 10.1088/1751-8121/ae3ff7

L. J. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, “Generalized hybrid momentum maps and reduction by symmetries of simple hybrid forced mechanical systems”, J. Math. Phys. 66(6), June 2025, doi: 10.1063/5.0178542

L. Colombo, M. de León, M. Lainz and A. López-Gordón, “Liouville-Arnold theorem for homogenous symplectic and contact Hamiltonian systems”, Geom. Mech. 02(03), pp. 275-307, 2025, doi: 10.1142/S2972458925400039.

L. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, “Hamilton-Jacobi theory for nonholonomic and forced hybrid mechanical systems”, Geom. Mech. 01(02), July 2024, doi: 10.1142/S2972458924500059.

M. de León, M. Lainz, A. López-Gordón and J. C. Marrero, “A new perspective on nonholonomic brackets and Hamilton-Jacobi theory”, J. Geom. Phys. 198, 105116, Feb. 2024, doi:10.1016/j.geomphys.2024.105116.

J. Gaset, A. López-Gordón and X. Rivas, “Symmetries, conservation and dissipation in time-dependent contact systems”, Fortschr. Phys. 71 (8-9), p. 2300048, May 2023, doi: 10.1002/prop.202300048.

M. de León, M. Lainz, A. López-Gordón and X. Rivas, “Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems”, J. Geom. Phys., 187, Feb. 2023, doi: 10.1016/j.geomphys.2023.104787.

L. J. Colombo, M. de León and A. López-Gordón, “Contact Lagrangian systems subject to impulsive constraints”, J. Phys. A: Math. Theor., 55(42), p. 425203, Oct. 2022, doi: 10.1088/1751-8121/ac96de.

M. de León, M. Lainz and A. López-Gordón, “Discrete Hamilton–Jacobi theory for systems with external forces”, J. Phys. A: Math. Theor., 55(20), p. 205201, Mar. 2022, doi: 10.1088/1751-8121/ac6240.

M. de León, M. Lainz and A. López-Gordón, “Geometric Hamilton–Jacobi theory for systems with external forces”, J. Math. Phys., 63(2), p. 022901, Feb. 2022, doi: 10.1063/5.0073214.

M. de León, M. Lainz and A. López-Gordón, "Symmetries, constants of the motion, and reduction of mechanical systems with external forces”, J. Math. Phys., 62(4), p. 042901, Apr. 2021, doi: 10.1063/5.0045073.

Conference papers

L. Colombo, M. E. Eyrea Irazú, M. E. García, A. López-Gordón, and M. Zuccalli, "Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps", in Geometric Science of Information, F. Nielsen and F. Barbaresco, Eds, Cham: Springer Nature Switzerland, Oct. 2025, pp. 303–310. doi: 10.1007/978-3-032-03924-8_31.

L. Colombo, M. de León, M. E. Eyrea Irazú, and A. López-Gordón, "Homogeneous bi-Hamiltonian structures and integrable contact systems", in Geometric Science of Information, F. Nielsen and F. Barbaresco, Eds, Cham: Springer Nature Switzerland, Oct. 2025, pp. 30–39. doi: 10.1007/978-3-032-03924-8_4.

A. López-Gordón and L. J. Colombo, “On the integrability of hybrid Hamiltonian systems”, 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024, IFAC-PapersOnLine, vol. 58, no. 6, pp. 83–88, 2024, doi: 10.1016/j.ifacol.2024.08.261.

M. de León, M. Lainz, A. López-Gordón and J. C. Marrero, “Nonholonomic brackets: Eden revisited”, Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol. 14072. Springer, Cham, 2023, pp. 105-112, doi: 10.1007/978-3-031-38299-4_12.

A. Anahory Simoes, A. López-Gordón, A. Bloch and L. Colombo, “Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage”, 2023 American Control Conference (ACC), San Diego, CA, USA, 2023, pp. 4587-4592, doi: 10.23919/ACC55779.2023.10156020.

A. López-Gordón, L. Colombo and M. de León, “Nonsmooth Herglotz variational principle”, 2023 American Control Conference (ACC), San Diego, CA, USA, 2023, pp. 3376-3381, doi: 10.23919/ACC55779.2023.10156228.

M. E. Eyrea Irazú, A. López-Gordón, L. J. Colombo and M. de León, “Hybrid Routhian reduction for simple hybrid forced Lagrangian systems”, 2022 European Control Conference (ECC), London, United Kingdom, 2022, doi: 10.23919/ECC55457.2022.9838077.

Theses

“The geometry of dissipation”, PhD Thesis, Universidad Autónoma de Madrid, September 2024, arXiv:2409.11947 [math.ph].

“The geometry of Rayleigh dissipation”, Master's Thesis, Universidad Autónoma de Madrid, July 2021, arXiv:2107.03780 [physics.class-ph].

“Study of the Entanglement Entropy of the XX Model”, Bachelor's Thesis, Universidad Complutense de Madrid, July 2020, doi: 10.13140/RG.2.2.24773.88809.

Collaborators

Some colleagues I currently collaborate or have collaborated with are:

• Jaime Bajo Da Costa (master's student at ETH Zürich, Switzerland)
• Leonardo Jesús Colombo (Centre of Automation and Robotics, CSIC, Spain)
• Manuel de León Rodríguez (Institute of Mathematical Sciences [CSIC] and Royal Academy of Sciences, Madrid, Spain)
• Javier de Lucas Araujo (Department of Mathematical Methods in Physics, University of Warsaw, Poland)
• María Emma Eyrea Irazú (CONICET-CMaLP-Dept. Mathematics, UNLP, Argentina)
• Jordi Gaset Rifà (Department of Mathematics, CUNEF University, Madrid, Spain)
• Janusz Roman Grabowski (Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland)
• Luis Alberto Ibort Latre (Carlos III University and Institute of Mathematical Sciences, Madrid, Spain)
• Rubén Izquierdo López (Institute of Mathematical Sciences (CSIC), Madrid, Spain)
• Víctor Manuel Jiménez Morales (Dept. of Fundamental Mathematics, National Univ. of Distance Education, Madrid, Spain)
• Manuel Lainz Valcázar (Department of Mathematics, CUNEF University, Madrid, Spain)
• Juan Carlos Marrero González (Dept. of Mathematics, Statistic and Operational Research, U. de La Laguna, Spain)
• Xavier Rivas Guijarro (Dept. d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain)
• Nicola Sansonetto (Department of Computer Science, University of Verona, Italy).
• María Cristina Sardón Muñoz (Technical University of Madrid, Spain)
• Bartosz Maciej Zawora (Mathematics Department, KU Leuven, Belgium)
• Xuefeng Zhao (College of Mathematics, Jilin University, Changchun, China)