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

Abstract

Sharkovskii 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 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 of
a quantum chaotic physical system called the kicked accelerated particle.