Shadowing by non-uniformly hyperbolic periodic points and uniform hyperbolicity
نویسندگان
چکیده
منابع مشابه
Shadowing by Non Uniformly Hyperbolic Periodic Points and Uniform Hyperbolicity
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context.
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We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2006
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/20/1/005