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

Abstract

Sharkovskiĭ proved that the existence of a periodic orbit of period which is not a power of 2 in a one-dimensional dynamical system implies existence of infinitely many periodic orbits. We obtain an analog of Sharkovskiĭ'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 of a quantum chaotic physical system called the kicked accelerated particle.