Diffeomorphisms of surfaces and their nonwandering sets
Diffeomorphisms of surfaces and their nonwandering sets
The purpose of this thesis is to examine some techniques which allow us to reduce the set t1 of non-wandering points of a diffeomorphism in its isotopy class, and to study the resulting diffeomorphism. In Chapter I we develop a technique to prove that for any manifold M there exists a diffeomorphism f isotopic to the identity such that S2(f) = p (a point). In Chapter II we study vector fields on two - manifolds, such that their fl set is a point. We also study the periodic data of Morse-Smale diffeomorphisms isotopic to an isometry with S1 minimal. In Chapter III we show how to apply the DA (Derived from Anosov) construction to Pseudo-Anosov maps, obtaining in this way an Axiom A diffeomorphism isotopic to a given Pseudo-Anosov map and we prove that the entropy of such Axiom A diffeomorphism is the same that the entropy of the Pseudo-Anosov map.
University of Southampton
Sienra Loera, Guillermo Javier Francisco
1980
Sienra Loera, Guillermo Javier Francisco
Sienra Loera, Guillermo Javier Francisco
(1980)
Diffeomorphisms of surfaces and their nonwandering sets.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The purpose of this thesis is to examine some techniques which allow us to reduce the set t1 of non-wandering points of a diffeomorphism in its isotopy class, and to study the resulting diffeomorphism. In Chapter I we develop a technique to prove that for any manifold M there exists a diffeomorphism f isotopic to the identity such that S2(f) = p (a point). In Chapter II we study vector fields on two - manifolds, such that their fl set is a point. We also study the periodic data of Morse-Smale diffeomorphisms isotopic to an isometry with S1 minimal. In Chapter III we show how to apply the DA (Derived from Anosov) construction to Pseudo-Anosov maps, obtaining in this way an Axiom A diffeomorphism isotopic to a given Pseudo-Anosov map and we prove that the entropy of such Axiom A diffeomorphism is the same that the entropy of the Pseudo-Anosov map.
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Published date: 1980
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Local EPrints ID: 459848
URI: http://eprints.soton.ac.uk/id/eprint/459848
PURE UUID: 614c7b84-b753-4577-82f5-21927d340993
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Date deposited: 04 Jul 2022 17:20
Last modified: 04 Jul 2022 17:20
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Author:
Guillermo Javier Francisco Sienra Loera
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