Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces
Mathematical Physics
2019-11-19 v1 Classical Analysis and ODEs
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Classical Physics
Abstract
Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By means of the Poincar\'{e}-Pontryagin theory, the existence of limit cycles on the invariant Casimir surfaces for the perturbed system is investigated up to first order of perturbation, providing sharp bounds for their number. Examples are given.
Keywords
Cite
@article{arxiv.1910.07264,
title = {Perturbed Euler top and bifurcation of limit cycles on invariant Casimir surfaces},
author = {Isaac A. García and Benito Hernández-Bermejo},
journal= {arXiv preprint arXiv:1910.07264},
year = {2019}
}