Transitivity and the existence of horseshoes on the 2-torus

Abstract

We study the relationship between transitivity and topological chaos for homeomorphisms of the two torus. We show that if a transitive homeomorphism of ${\mathbb{T}}^2$ is homotopic to the identity and has both a fixed point and a periodic point which is not fixed, then it has a topological horseshoe. We also show that if a transitive homeomorphims of ${\mathbb{T}}^2$ is homotopic to a Dehn twist, then either it is aperiodic or it has a topological horseshoe.

To appear in Nonlinearity

References in corpus (3)

• Strictly Toral Dynamics
• Dynamics of homeomorphisms of the torus homotopic to Dehn twists
• On annular maps of the torus and sublinear diffusion