Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm
Geometric Topology
2011-12-06 v3 Dynamical Systems
Abstract
Sharkovskii proved that the existence of a periodic orbit in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of shear homeomorphisms of the torus. This is done by obtaining a dynamical order relation on the set of simple orbits and simple pairs. We then use this order relation for a global analysis for a quantum chaotic physical system called the kicked accelerated particle.
Keywords
Cite
@article{arxiv.0704.1272,
title = {Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm},
author = {Tali Pinsky and Bronislaw Wajnryb},
journal= {arXiv preprint arXiv:0704.1272},
year = {2011}
}
Comments
31 pages, 24 figures, to appear in Topological Methods in Nonlinear Analysis