Asier López-Gordón

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

Publications

Preprints

J. Grabowski and A. López-Gordón, “A Darboux classification of homogeneous Pfaffian forms on graded manifolds”, Feb. 2026, arXiv:2602.04671 [math.DG]

L. Colombo and A. López-Gordón, “Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad Structure”, Jan. 2026, arXiv:2601.03041 [math-ph]

Journal articles

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)
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).
Bartosz Maciej Zawora (Department of Mathematical Methods in Physics, University of Warsaw, Poland)