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Master's Dissertation
DOI
10.11606/D.55.2013.tde-20032013-160120
Document
Author
Full name
Jorge Luis Crisostomo Parejas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Tahzibi, Ali (President)
Apaza, Carlos Alberto Maquera
Kocsard, Alejandro
Title in Portuguese
Medidas transversas, correntes e sistemas dinâmicos
Keywords in Portuguese
Cohomologia de DeRham
Correntes
Difeomorfismos e medida de máxima entropia
Medidas transversas invariantes
Abstract in Portuguese
Neste trabalho, fazemos um estudo das correntes e das medidas transversas invariantes por holonomia, e mostraremos o resultado de D. Sullivan [23] sobre a correspondência biunívoca entre estes dois objetos. Em particular mostraremos um resultado conhecido de J. Plante [17] sobre a existência de medidas transversas invariantes sob a hipótese de crescimento sub-exponencial. Apresentamos também, o resultado devido a Ruelle-Sullivan [19] de que a medida de máxima entropia de um difeomorfismo topologicamente mixing pode-se expressar como o produto de duas medidas transversas invariantes para as folheações estáveis e instáveis. Por último, mostramos que os difeomorfismos de Anosov topologicamente mixing, que preservam a orientação das folhas estáveis e folhas instáveis induzem elementos da cohomologia de DeRham
Title in English
Transverse measures, currents and dynamical systems
Keywords in English
Currents
DeRham cohomology
Diffeomorphism and maximum entropy measure
Invariant transverse measure
Abstract in English
In this work, we make a study of currents and holonomy invariant transverse measure, and we will show the result of D. Sullivan [23] about the biunivocal correspondence between these two objects. In particular we show a known result of J. Plante [17] about the existence of invariant transverse measures under the hypothesis of sub-exponential growth. Also we will present, the result due to Ruelle-Sullivan [19] that the maximum entropy measure of a diffeomorphism topologically mixing can be expressed as the product of two invariant transverse measures for stable and unstable foliations. Finally, we show that the Anosov diffeomorphisms topologically mixing, which preserve the orientation of the leaves stable and unstable induce elements DeRham cohomology
 
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jorgerevisada.pdf (1.78 Mbytes)
Publishing Date
2013-03-20
 
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