Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm

Details Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm Dynamics of shear homeomorphisms of tori and the Bestvina-Handel algorithm

2007-04-10

arxiv.org/abs/0704.1272v3

Mathematics

Geometric Topology

31 pages, 24 figures, to appear in Topological Methods in Nonlinear Analysis

Scientific paper

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.

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