Asier López-Gordón

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
—Eugene Wigner, Comm. Pure Appl. Math., 13:1-14 (1960)

Research interests

My general area of interest is differential geometry and its applications to mathematical physics, control theory and dynamical systems. More specifically, my work concerns the geometrical aspects of non-conservative mechanical systems. I'm particularly interested in the symmetries, integrability and reduction methods for such systems.

Related topics include:

Profiles

Publications

Preprints

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M. de León, M. Lainz, A. López-Gordón and J. C. Marrero, ‘Nonholonomic brackets: Eden revisited’, Mar. 2023, arXiv:2303.03002 [math-ph].
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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].
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L. Colombo, M. de León, M. E. Eyrea Irazú and A. López-Gordón, ‘Geometric Hamilton-Jacobi theory and integrability for nonholonomic and forced hybrid systems’, Nov. 2022, arXiv:2211.06252 [math-ph].
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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

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J. Gaset, A. López-Gordón and X. Rivas, ‘Symmetries, conservation and dissipation in time-dependent contact systems’, Fortschr. Phys. 2023, 2300048, doi: 10.1002/prop.202300048.
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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.
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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.
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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.
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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.
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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

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A. Anahory Simoes, A. López-Gordón, A. Bloch, L. Colombo, ‘Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage’, Sept. 2022, 2023 American Control Conference (ACC) (to appear), arXiv:2209.14255 [eess.SY].
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A. López-Gordón, L. Colombo and M. de León, ‘Nonsmooth Herglotz variational principle’, Aug. 2022, 2023 American Control Conference (ACC) (to appear), arXiv:2208.02033 [math.OC].
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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), pp. 345-350, July 2022, doi: 10.23919/ECC55457.2022.9838077.

Theses

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‘The geometry of Rayleigh dissipation’, Master’s Thesis, Universidad Autónoma de Madrid, July 2021, arXiv:2107.03780 [physics.class-ph].
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‘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)
  • Anthony M. Bloch (Dept. of Mathematics, University of Michigan, USA)
  • Leonardo J. Colombo (Centre of Automation and Robotics, CSIC, Spain)
  • Manuel de León (ICMAT, CSIC, Spain)
  • Javier de Lucas Araujo (Dept. of Mathematical Methods in Physics, University of Warsaw, Poland)
  • Mᵃ Emma Eyrea Irazú (CONICET-CMaLP-Dept. Mathematics, UNLP, Argentina)
  • Jordi Gaset (Dpto. Matemática Aplicada, ETSI Montes, Forestal y del Medio Natural, Universidad Politécnica de Madrid, Madrid, Spain)
  • Manuel Lainz (ICMAT, CSIC, Spain)
  • Juan Carlos Marrero (Department of Mathematics, Statistic and Operational Research, Universidad de La Laguna, Spain)
  • Xavier Rivas (Escuela Superior en Ingeniería y Tecnología, Universidad Internacional de la Rioja, Spain)
  • Bartosz M. Zawora (Dept. of Mathematical Methods in Physics, University of Warsaw, Poland)