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

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.

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

References in corpus (2)

• The set of badly approximable vectors is strongly $C^1$ incompressible
• Modified Schmidt games and non-dense forward orbits of partially hyperbolic systems