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Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity

Armando Castro·Krerley Oliveira·Vilton Pinheiro
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Abstract

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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Armando Castro, Krerley Oliveira, Vilton Pinheiro. 2006-06-01. Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity. https://doi.org/10.1088/0951-7715%2F20%2F1%2F005

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