Nondense orbits for Anosov diffeomorphisms of the $2$-torus

Jimmy Tseng

Nondense orbits for Anosov diffeomorphisms of the $2$-torus

Dynamical Systems 2016-01-29 v2

Authors: Jimmy Tseng

Abstract

Let $\lambda$ denote the probability Lebesgue measure on ${\mathbb T}^2$ . For any $C^2$ -Anosov diffeomorphism of the $2$ -torus preserving $\lambda$ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result in~\cite[Theorem~1.4]{T4} for $C^2$ -expanding maps of the circle.

Keywords

Anosov diffeomorphisms nondense orbits 2-torus hyperplane absolute winning Lebesgue measure entropy

Cite

@article{arxiv.1503.02273,
  title  = {Nondense orbits for Anosov diffeomorphisms of the $2$-torus},
  author = {Jimmy Tseng},
  journal= {arXiv preprint arXiv:1503.02273},
  year   = {2016}
}

Comments

Minor typos corrected. Added more exposition

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