Towers of finite type complex analytic maps.

Title: Towers of finite type complex analytic maps.
Identifier: AAI9405521
identifier: 9405521
Creator: Epstein, Adam Lawrence.
Contributor: Adviser: Dennis Sullivan
Date: 1993
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: An analytic map {dollar}f : W \to X{dollar} of complex 1-manifolds is said to be of finite type if X is compact and f is an even cover near all but finitely many singular values in X; when {dollar}W \subseteq X,{dollar} the iterates of f constitute a one-generator dynamical system. We extend the three core principles of rational dynamics: (1) The density of repelling periodic points in the Julia set, (2) The standard classification of periodic components of the Fatou set, (3) The nonexistence of wandering components, to finite type maps. Our results apply more generally to countably generated towers constructed inductively from finite type maps. Such towers can be geometric limits of sequences of one-generator systems.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.