Real Analysis Exchange

Nondense Orbits for Anosov Diffeomorphisms of the $2$-Torus

Jimmy Tseng

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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 of Tseng (2009) for $C^2$-expanding maps of the circle.

Article information

Source
Real Anal. Exchange, Volume 41, Number 2 (2016), 307-314.

Dates
First available in Project Euclid: 30 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rae/1490839333

Mathematical Reviews number (MathSciNet)
MR3597322

Zentralblatt MATH identifier
1384.37039

Subjects
Primary: 37D05: Hyperbolic orbits and sets
Secondary: 28A78: Hausdorff and packing measures

Keywords
nondense orbits Anosov diffeomorphisms winning sets

Citation

Tseng, Jimmy. Nondense Orbits for Anosov Diffeomorphisms of the $2$-Torus. Real Anal. Exchange 41 (2016), no. 2, 307--314. https://projecteuclid.org/euclid.rae/1490839333


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