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. I am also fascinated by graded manifolds and their applications to classical differential geometry and parastatistics.

In my doctoral dissertation, titled The geometry of dissipation (arXiv:2409.11947), I consider 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, three classes of geometric frameworks modeling dissipative systems are explored: systems with external forces, contact systems, and systems with impacts.

Profiles

Publications

Preprints

PDF
L. Colombo, M. de León, M. Lainz and A. López-Gordón, “Liouville-Arnold theorem for contact Hamiltonian systems”, Feb. 2023, arXiv:2302.12061 [math.SG].
PDF
L. J. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, “Generalized hybrid momentum maps and reduction by symmetries of forced mechanical systems with inelastic collisions”, June 2022, arXiv:2112.02573 [eess.SY].

Journal articles

PDF
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; arXiv:2211.06252 [math-ph].
PDF
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.
PDF
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.
PDF
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.
PDF
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.
PDF
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.
PDF
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.
PDF
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

PDF
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.
PDF
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.
PDF
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.
PDF
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.
PDF
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

PDF
“The geometry of dissipation”, PhD Thesis, Universidad Autónoma de Madrid, September 2024, arXiv:2409.11947 [math.ph].
PDF
“The geometry of Rayleigh dissipation”, Master's Thesis, Universidad Autónoma de Madrid, July 2021, arXiv:2107.03780 [physics.class-ph].
PDF
“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 of the colleagues I currently collaborate or have collaborated with are:

  • Alexandre Anahory Simões (School of Science and Technology, IE University, Spain)
  • Leonardo J. Colombo (Centre of Automation and Robotics, CSIC, Spain)
  • Manuel de León (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)
  • Mᵃ Emma Eyrea Irazú (CONICET-CMaLP-Dept. Mathematics, UNLP, Argentina)
  • Jordi Gaset (Department of Quantitative Methods, CUNEF University, Madrid, Spain)
  • Katarzyna Grabowska (Department of Mathematical Methods in Physics, University of Warsaw, Poland)
  • Janusz Grabowski (Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland)
  • Víctor M. Jiménez (Dept. of Fundamental Mathematics, National Univ. of Distance Education, Madrid, Spain)
  • Manuel Lainz (Department of Quantitative Methods, CUNEF University, Madrid, Spain)
  • Juan Carlos Marrero (Dept. of Mathematics, Statistic and Operational Research, U. de La Laguna, Spain)
  • Xavier Rivas (Escuela Superior en Ingeniería y Tecnología, Universidad Internacional de la Rioja, Spain)
  • Bartosz M. Zawora (Department of Mathematical Methods in Physics, University of Warsaw, Poland)