Dynamical models for some torus homeomorphisms

TL;DR

This paper explores the existence of topological dynamical models for rotation sets of torus homeomorphisms, extending concepts from circle dynamics to two-dimensional cases.

Contribution

It provides new results on the existence of topological models linked to rotation sets for torus homeomorphisms, broadening understanding beyond circle dynamics.

Findings

Results on the existence of topological models for rotation sets

Extension of circle homeomorphism concepts to the torus

Insights into the dynamics of torus homeomorphisms

Abstract

It is well known that the rotation number of a circle homeomorphism defined by H. Poincar\'e allows to completely understand the dynamics of such a map from the topological point of view. In this paper, we collect some results concerning the existence of topological dynamical models associated to rotation sets of homeomorphisms of $\T^2$.