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Ruben Flores-Espinoza

Publications and source records attributed to Ruben Flores-Espinoza.

2 recordsLinked to original sources
arXiv2013

The Lie Transform Method for perturbations of contravariant antisymmetric tensor fields and its applications to Hamiltonian dynamics

By means of the Schouten calculus for contravariant antisymmetric tensor fields, we apply the Lie transform method to investigate smooth deformations of tensor fields and, in particular, to perturbations of Hamiltonian systems generated by deformations of the Poisson bracket. Using results by Karasev and Vorobiev on the computation of Poisson cohomology we describe infinitesimal generators for the Lie transformations. We give applications to perturbed Euler equations on six dimensional Lie coalgebras and to Hamiltonian systems on Poisson manifolds equipped with Dirac brackets.

math-ph↗
arXiv2010

Periodic first integrals for Hamiltonian systems of Lie type

We prove the existence of a Lie algebra of first integrals for time dependent Hamiltonian systems of Lie type. Moreover, applying the Floquet theory for periodic Euler systems on Lie algebras, we show the existence of an abelian Lie algebra of periodic first integrals for periodic Hamiltonian systems. An application to the dynamics of a nonlinear oscillator is given.

math-ph↗