Dynamical Properties of Gaussian Thermostats
Dynamical Systems
2013-11-01 v1
Abstract
In this work we show that the set of Kupka-Smale Gaussian thermostats on a compact manifold is generic. A Gaussian thermostat is Kupka-Smale if the closed orbits are hyperbolic and the heteroclinic intersection are transversal. We also show a dichotomy between robust transitivity and existence of arbitrary number of attractors or repellers orbits. The main tools are the concept of transitions adapted to the conformally symplectic context and a perturbative theorem which is a version of the Franks lemma for Gaussian thermostats. Finally we provide some conditions in terms of geometrical invariants for an invariant set of a Gaussian thermostat to have dominated splitting. From that we conclude some dynamical properties for the surface case.
Keywords
Cite
@article{arxiv.1310.8542,
title = {Dynamical Properties of Gaussian Thermostats},
author = {Ivana Latosinski and Enrique Pujals},
journal= {arXiv preprint arXiv:1310.8542},
year = {2013}
}