Topological Invariance Of The Non-uniform Hyperbolicity Condition For Rational Function

In this thesis we mainly study the topological invariance of the non-uniform hyperbolicity condition for rational function.we all know that CE condition is common non-uniform hyperbolicity condition.In the case of maps with several critical points Collet-Eckmann condition is not in itself invariance under topological conjugacy.Previous results indicate that three strengthened version of the Collet-Eckmann condition for multimodal interval maps is topologically invariant.This thesis proves the conclusion are tenable for the case of rational maps.The thesis contains three chapters.In chapter 1,we briefly recall the origin,development and some background knowledge related to this article,and we introduce some notations,basic concepts,and the main results of the thesis.In chapter 2,we review some preliminary notations and results in complex analysis and complex dynamics.In chapter 3,we mainly study the topological invariance of CE condition for a rational map of degree at least 2.