Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity
Dynamical Systems
2009-11-11 v1
Abstract
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map 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.
Cite
@article{arxiv.math/0606029,
title = {Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity},
author = {Armando Castro and Krerley Oliveira and Vilton Pinheiro},
journal= {arXiv preprint arXiv:math/0606029},
year = {2009}
}