Pruning fronts and the formation of horseshoes.

Title: Pruning fronts and the formation of horseshoes.
Identifier: AAI9605586
identifier: 9605586
Creator: de Carvalho, Andre Salles.
Contributor: Adviser: Dennis Sullivan
Date: 1995
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: Let {dollar}f:\pi\to\pi{dollar} be a homeomorphism of the plane {dollar}\pi.{dollar} We define open sets P, called pruning fronts after the work of Cvitanovic (C), for which it is possible to construct an isotopy {dollar}H:\pi\times\lbrack0,\ 1\rbrack\to\pi{dollar} with open support contained in {dollar}\bigcup\sb{lcub}\scriptstyle n\in\doubz{rcub} f\sp{lcub}n{rcub}(P){dollar} such that {dollar}H({lcub}\cdot{rcub}, 0) = f({lcub}\cdot{rcub}){dollar} and {dollar}H({lcub}\cdot{rcub}, 1) = f\sb{lcub}P{rcub}({lcub}\cdot{rcub}),{dollar} where {dollar}f\sb{lcub}P{rcub}{dollar} is a homeomorphism under which every point of P is wandering. Applying this construction with f being Smale's horseshoe, it is possible to obtain an uncountable family of homeomorphisms, depending on infinitely many parameters, going from trivial to chaotic dynamic behaviour. This family is a 2-dimensional analog of a 1-dimensional universal family.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.