On conjugacies of infinitely renormalizable maps.

Title: On conjugacies of infinitely renormalizable maps.
Identifier: AAI9304715
identifier: 9304715
Creator: Paluba, Waldemar.
Contributor: Adviser: Dennis P. Sullivan
Date: 1992
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The properties of the conjugacies between infinitely renormalizable maps of an interval are studied here. In the main part of the work we deal with the renormalization with uniformly bounded return time. For such maps we show the conjugacies, that a priori are arbitrary homeomorphisms, to be quasisymmetric on the whole domain intervals.;Subsequently, we examine the properties of these conjugacies reduced to smaller domains, namely the closures of the orbits of critical points. Here we show that the classes of Lipschitz continuous equivalence coincide with the classes of {dollar}C\sp1{dollar}-smooth equivalence. The proof is based on a more general argument asserting that bilipschitz continuous conjugacies between two {dollar}\omega{dollar}-limit sets containing dense subsets of preimages of respective critical points are differentiable with nonvanishing derivative at either of the critical points.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.