Locally expanding mappings and hyperbolicity

Jacek Tabor

DOI: http://dx.doi.org/10.12775/TMNA.2007.032

Abstract


The aim of the following paper is to propose and investigate the
partial generalization of hyperbolicity to metric spaces. The
locally expanding mappings, as we call them, possess many similar
behaviour to that characteristic to hyperbolic mappings, in
particular, they have lipschitz shadowing property. As a direct
corollary we obtain for example shadowing on the Julia set.

Keywords


Stability; hyperbolicity; shadowing; Julia set

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