Research

My research is mainly concerned with the geometry and dynamics of mechanical systems with symmetry.

Publication list.

2021-Present

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. arXiv: 2404.14156 (2024). (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. arXiv: 2309.11597 (2023). (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-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)
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)
García-Naranjo L.C. and Marrero J.C., The geometry of nonholonomic Chaplygin systems revisited. Nonlinearity 33 (2020) 1297-1341. (paper)
García-Naranjo L.C., Integrability of the n-dimensional axially symmetric Chaplygin sphere. Reg. and Chaot. Dyn. 24 (2019) 450-463. (paper)
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)
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)
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)
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)
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)
García-Naranjo L.C. and Montaldi J., Gauge Momenta as Casimir functions of nonholonomic systems. Arch. Rat. Mech. Anal. 228 (2018) 563-602. (paper)
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)
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)
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)