Continuous inverse shadowing and hyperbolicity
نویسندگان
چکیده
منابع مشابه
Continuous Inverse Shadowing and Hyperbolicity
We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.
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We define continuous and inverse shadowing for flows and prove some properties. In particular, we will prove that an expansive flow without fixed points on a compact metric space which is a shadowing is also a continuous shadowing and hence an inverse shadowing (on a compact manifold without boundary).
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Preface In the beginning of 90s the authors of this monograph proposed a generalization of the concept of hyperbolicity, first for differentiable mappings and later for Lipschitz mappings, which they called 'semi-hyperbolicity'. This arose indirectly in the context of their research at that time on the effect of spatial discretization on the behavior of a dynamical system, in particular that of...
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We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.
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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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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2003
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700033487