Nondense orbits for Anosov diffeomorphisms of the 2-torus

Jimmy Tseng

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Let λ denote the probability Lebesgue measure on Τ2. 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.
Original languageEnglish
Pages (from-to)307-314
Number of pages8
JournalReal Analysis Exchange
Volume41
Issue number2
Publication statusPublished - 2016

Keywords

  • Nondense orbits
  • Anosov diffeomorphisms
  • Winning sets

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