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Doctoral Thesis
DOI
10.11606/T.55.2010.tde-05062010-173022
Document
Author
Full name
Bernardo Paschoarelli Veiga Gomes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Zanata, Salvador Addas (President)
Kocsard, Alejandro
Brandão, Daniel Smania
Koropecki, Andrés
Tal, Fabio Armando
Title in Portuguese
A versão discreta da conjectura de Markus-Yamabe
Keywords in Portuguese
Condições espectrais
Estabilidade global
Sistemas dinâmicos
Abstract in Portuguese
O principal objetivo desta tese é estudar os difeomorfismos planares que satisfazem as hipóteses da Versão Modificada da Conjectura Discreta de Markus-Yamabe. Para estes difeomorfismos, definimos um conceito construtivo de número de rotação. Além disto, exibimos um contra-exemplo para a Versão Modificada da Conjectura Discreta de Markus-Yamabe que apresenta uma intersecção homoclínica transversal e implica a existência de infinitos pontos periódicos hiperbólicos
Title in English
The modified version of the discrete conjecture of Markus-Yamabe
Keywords in English
Dynamical systems
Global stability
Spectral conditions
Abstract in English
The main goal of this thesis is to study the plane diffeomorphisms satisfying the hypothesis of the Modified Version of the Discrete Conjecture of Markus-Yamabe. For these diffeomorphisms, we define a constructive concept of rotation number. Moreover, we present a counter-example to the Modified Version of the Discrete Markus-Yamabe Conjecture which exhibits a transversal homoclinic intersection, implying the existence of infinitely many hyperbolic periodic points
 
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Publishing Date
2010-10-06
 
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