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Article overview
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On non-dense orbits of certain non-algebraic dynamical systems | | Weisheng Wu
; | | Date: |
29 Jul 2015 | | Abstract: | We show that the set of points with non-dense forward orbit under a
$C^{1+ heta}$-Anosov diffeomorphism with conformality on unstable manifolds is
a winning set for Schmidt games. We also show that for a
$C^{1+ heta}$-expanding endomorphism the set of points with non-dense forward
orbit is a winning set for certain variants of Schmidt games. These generalize
some results of J. Tseng in cite{tseng} and cite{tseng1} for $C^2$-expanding
endomorphisms on the circle and certain Anosov diffeomorphisms on the
$2$-torus. | | Source: | arXiv, 1507.8149 | | Services: | Forum | Review | PDF | Favorites | |
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