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arXiv · 2206.02740

Transitivity and the existence of horseshoes on the 2-torus

Pollyanna Vicente Nunes·Fabio Armando Tal
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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.

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Pollyanna Vicente Nunes, Fabio Armando Tal. 2022-06-06. Transitivity and the existence of horseshoes on the 2-torus. https://doi.org/10.1088/1361-6544/aca252

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