Nondense orbits for Anosov diffeomorphisms of the 2-torus

2015/03/08 by Tseng, Jimmy · 1 citation
#28A78 #37D05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.02273

Abstract

Let λ denote the probability Lebesgue measure on \mathbb T². For any C²-Anosov diffeomorphism of the 2-torus preserving λ 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 C²-expanding maps of the circle.

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