Locally expanding mappings and hyperbolicity - Tabor, Jacek (Topological Methods in Nonlinear Analysis, 2007)
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.