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, 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. During my postdoctoral period, I plan to focus my research on two main lines: integrable contact Hamiltonian systems and graded 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

Preprints

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].

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

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. (to appear), doi: 10.1142/S2972458924500059; arXiv:2211.06252 [math-ph].

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

A. López-Gordón and L. J. Colombo, “On the integrability of hybrid Hamiltonian systems”, Accepted on the Proceedings of the 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, arXiv:2307.06049 [math-ph].

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 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 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)