Nondense orbits for Anosov Diffeomorphisms of the 2-Torus
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Let λ denote the probability Lebesgue measure on 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 [18, Theorem 1.4] for C2-expanding maps of the circle.
The author acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 291147.
This is the author accepted manuscript.
Vol. 41, pp. 307 - 314