My research is mainly concerned with the geometry and dynamics of mechanical systems with symmetry.
Publication list.
2021-Present
- Costa Villegas M. and García-Naranjo L.C., Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane.
arXiv: 2409.08072 (2024). (preprint)
- Constantineau K., García-Azpeitia C., García-Naranjo L.C. and Lessard J.P., Determination of stable branches of relative equilibria of the N-vortex problem on the sphere.
arXiv: 2309.04320 (2023). (preprint)
- García-Naranjo L.C., Marrero J.C., Martín de Diego D. and Petit Valdés E.P., Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation.
.
J. Nonlinear Sci.
34
110 (2024). (paper)
- García-Naranjo L.C., Ortega R. and Ureña A.J., Invariant measures as obstructions to attractors in dynamical
systems and their role in nonholonomic mechanics.
Reg. and Chaot. Dyn.
29
(2024) 751-763. (paper)
- García-Azpeitia C. and García-Naranjo L.C., Platonic solids and symmetric solutions of the N-vortex problem in the sphere.
J. Nonlinear Sci.
32
39 (2022). (paper)
- García-Naranjo L.C. and Vermeeren M., Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics.
J. Comput. Dyn.
8
(2021) 241-271. (paper)
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García-Naranjo L.C. and Montaldi J., Attracting and repelling 2-body problems on a family of surfaces of constant curvature.
J. Dyn. Diff. Equat.
33
1579-1603 (2021). (paper)
2016-2020
- García-Naranjo L.C., Some remarks about the centre of mass of two particles in spaces of constant curvature. J. Geom. Mech.
12 (2020) 435-446. (paper)
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García-Naranjo L.C. and Marrero J.C., The geometry of nonholonomic Chaplygin systems revisited.
Nonlinearity
33
(2020) 1297-1341. (paper)
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García-Naranjo L.C., Integrability of the n-dimensional axially symmetric Chaplygin sphere.
Reg. and Chaot. Dyn.
24
(2019) 450-463. (paper)
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García-Naranjo L.C., Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere.
Theoretical and Applied Mechanics
46
(2019) 65-88. (paper)
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García-Naranjo L.C., Generalisation of Chaplygin's Reducing Multiplier Theorem with an application to multi-dimensional nonholonomic dynamics.
J. Phys. A: Math. Theor.
52
(2019) 205203 (16pp). (paper)
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Fassò, F., García-Naranjo L. C., and Montaldi J., Integrability and dynamics of the n-dimensional symmetric Veselova top.
J. Nonlinear Sci.
29
(2019) 1205-1246. (paper)
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Borisov, A.V., García-Naranjo L.C., Mamaev I.S. and Montaldi J., Reduction and relative equilibria for the 2-body problem in spaces of constant curvature.
Celestial Mech. Dynam. Astronom.
130
(2018) 130:43. (paper)
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Fassò F., García-Naranjo L.C. and Sansonetto N., Moving energies as first integrals of nonholonomic systems with affine constraints.
Nonlinearity
31
(2018) 755-782. (paper)
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García-Naranjo L.C. and Montaldi J., Gauge Momenta as Casimir functions of nonholonomic systems.
Arch. Rat. Mech. Anal.
228
(2018) 563-602. (paper)
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García-Naranjo L.C. and Jiménez F., The geometric discretisation of the Suslov problem: a case study of consistency for nonholonomic integrators.
Disc. and Cont. Dyn. Syst. Series A
37
(2017), 4249-4275 (paper)
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García-Naranjo L.C., Montaldi J. and Smolyanov O.G., Transformations of Feynman path integrals and generalized densities of Feynman pseudomeasures.
Doklady Math.
93
(2016) 282-285. (paper)
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García-Naranjo L.C., Marrero J.C., Pérez-Chavela E. and Rodríguez-Olmos M., Classification and stability of relative equilibria for the 2-body problem in the hyperbolic space of dimension 2.
J. of Differential Equations
260
(2016) 6375-6404. (paper)
2011-2015
- Fassò F., García-Naranjo L.C. and Giacobbe A., Quasi-periodicity in relative quasi-periodic tori. Nonlinearity
28 (2015), 4281-4301. (paper)
- Bravo-Doddoli A. and García-Naranjo L.C., The dynamics of an articulated n-trailer vehicle. Reg. and Chaot. Dyn.
20 (2015), 497-517. (paper)
- García-Naranjo L.C., Suárez-Serrato P. and Vera R., Poisson structures on smooth 4-manifolds. Lett. in Math. Phys.
105 (2015), 1533-1550. (paper)
- Fedorov Y.N., García-Naranjo L.C. and Marrero J.C., Unimodularity and preservation of volumes in nonholonomic mechanics. J. Nonlinear Sci.
25 (2015), 203-246. (paper)
- García-Naranjo L.C., Maciejewski A.J., Marrero J.C. and Przybylska M., The inhomogeneous Suslov problem. Phys. Lett. A 378 (2014), 2389-2394. (paper)
- García-Naranjo L.C. and Marrero J.C., Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane. Reg. and Chaot. Dyn.
18 (2013), 372-379. (paper)
- García-Naranjo L.C. and Vankerschaver J., Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation. J. Geom. Phys. 73 (2013), 56-69. (paper)
- Fedorov Y.N., García-Naranjo L.C. and Vankerschaver J., The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation. Disc. and Cont. Dyn. Syst. Series A
33 (2013) no. 9, 4017-4040. (paper)
- Balseiro, P. and García-Naranjo, L.C., Gauge transformations, twisted Poisson brackets and Hamiltonization of nonholonomic systems. Arch. Rat. Mech. Anal.
205 (2012), no. 1, 267-310. (paper)
2010 and earlier
- Fedorov Y.N. and García-Naranjo, L.C., The hydrodynamic Chaplygin sleigh. J. Phys. A: Math. Theor.
43 (2010) 434013 (18pp). (paper)
- García-Naranjo, L. C., Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere. Disc. and Cont. Dyn. Syst. Series S, 3 (2010), no. 1, 37-60. (paper)
- Hochgerner S. and García-Naranjo, L.C., G-Chaplygin systems with internal symmetries, truncation, and an (almost) symplectic view of Chaplygin's ball. J. Geom. Mech.
1 (2009), no.1, 35-53. (paper)
- García-Naranjo, L. C., Reduction of almost Poisson brackets for nonholonomic systems on Lie groups. Reg. and Chaot. Dyn., 14 (2007), no. 4, 365-388. (paper)
- Tartakovsky A.M., García-Naranjo L.C., and Tartakovsky D.M., Transient Flow in a Heterogeneous Vadose Zone with Uncertain Parameters. Vadose Zone Journal, 3 (2004), 154-163. (paper)