Locally expanding mappings and hyperbolicity - Tabor, Jacek (Topological Methods in Nonlinear Analysis, 2007)
The aim of the following paper is to propose and investigate thepartial generalization of hyperbolicity to metric spaces. Thelocally expanding mappings, as we call them, possess many similarbehaviour to that characteristic to hyperbolic mappings, inparticular, they have lipschitz shadowing property. As a directcorollary we obtain for example shadowing on the Julia set.