### 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.

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.

#### Keywords

Torus homeomorphisms; dynamical systems; forcing; periodic orbits

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.