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arXiv · 1507.08149

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

Weisheng Wu
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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 $C^{1+θ}$-expanding endomorphism the set of points with non-dense forward orbit is a winning set for certain variants of Schmidt games.

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Weisheng Wu. 2015-12-27. On non-dense orbits of certain non-algebraic dynamical systems. https://arxiv.org/abs/1507.08149

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