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	MODIFIED SCHMIDT GAMES AND NON-DENSE FORWARD ORBITS OF PARTIALLY HYPERBOLIC SYSTEMS
	Wu, Weisheng
	2016
关键词	Schmidt games non-dense orbits partially hyperbolic diffeomorphism Hausdorff dimension BADLY APPROXIMABLE NUMBERS HAUSDORFF DIMENSION TORAL AUTOMORPHISMS HOMOGENEOUS SPACES BOUNDED ORBITS INVARIANT-SETS FLOWS DIFFEOMORPHISMS ENDOMORPHISMS ERGODICITY
英文摘要	Let f : M -> M be a C1+theta-partially hyperbolic diffeomorphism. We introduce a type of modified Schmidt games which is induced by f and played on any unstable manifold. Utilizing it we generalize some results of [25] as follows. Consider a set of points with non-dense forward orbit: E(f, y) := {z is an element of M : y is not an element of<({f(k)(z), k is an element of N}})over bar> for some y is an element of M and E-x(f, y) := E(f, y) boolean AND W-u(x) for any x is an element of M. We show that E-x (f, y) is a winning set for such modified Schmidt games played on W-u(x), which implies that E-x(f,y) has Hausdorff dimension equal to dim W-u(x). Then for any nonempty open set V subset of M we show that E(f, y) boolean AND v has full Hausdorff dimension equal to dim M, by using a technique of constructing measures supported on E(f, y) with lower pointwise dimension approximating dim M.; SCI(E); ARTICLE; wuweisheng@math.pku.edu.cn; 6; 3463-3481; 36
语种	英语
出处	SCI
出版者	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/438146]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wu, Weisheng. MODIFIED SCHMIDT GAMES AND NON-DENSE FORWARD ORBITS OF PARTIALLY HYPERBOLIC SYSTEMS. 2016-01-01.

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