On non-dense orbits of certain non-algebraic dynamical systems

Weisheng Wu

On non-dense orbits of certain non-algebraic dynamical systems

Dynamical Systems 2015-12-29 v3

Authors: Weisheng Wu

Abstract

In this paper, we manage to apply Schmidt games to certain non-algebraic dynamical systems. More precisely, we show that the set of points with non-dense forward orbit under a $C^2$ -Anosov diffeomorphism with conformality on unstable manifolds is a winning set for Schmidt games. It is also proved that for a $C^{1+\theta}$ -expanding endomorphism the set of points with non-dense forward orbit is a winning set for certain variants of Schmidt games.

Keywords

diffeomorphism groups dynamical systems and chaos

Cite

@article{arxiv.1507.08149,
  title  = {On non-dense orbits of certain non-algebraic dynamical systems},
  author = {Weisheng Wu},
  journal= {arXiv preprint arXiv:1507.08149},
  year   = {2015}
}

Comments

17 pages. arXiv admin note: text overlap with arXiv:1504.01835

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