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Master's Dissertation
DOI
10.11606/D.55.2013.tde-02102013-104602
Document
Author
Full name
Gabriel Elias Mantovani
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Tahzibi, Ali (President)
Baraviera, Alexandre Tavares
Varão Filho, José Régis Azevedo
Title in Portuguese
Teoria não comutativa de integração e dinâmica hiperbólica
Keywords in Portuguese
Desintegração
Dinâmica hiperbólica
Grupóides
Medidas SRB
Teoria não comutativa da integração
Abstract in Portuguese
Uma das caracterizações de medidas SRB é a de que a sua desintegração em relação as partições mensuráveis subordinadas as variedades instáveis são absolutamente continuas com respeito a medida Lebesgue nestas mesmas variedades. Este trabalho segue os passos de Segert [16] ao analisar a aplicabilidade da teoria de integração não comutativa de Alain Connes ao estudo de medidas SRB de sistemas dinâmicos hiperbólicos do tipo (M, f) com M uma variedade compacta e f um difeomorfismo 'C POT. 2'. Nesta dissertação é realizada a demonstração do teorema da desintegração de Rokhlin utilizando o conceito de esperança condicional. É fornecida uma introdução a teoria de integração não comutativa de Alain Connes. E apresenta-se uma injeção entre medidas SRB de sistemas dinâmicos hiperbólicos e as medidas transversas definidas sobre este sistema
Title in English
Non commutative integration theory and hyperbolic dynamic
Keywords in English
Desintegration
Hyperbolic dynamic
Non communitative integration theory
SRB measures
Abstract in English
A characterization of SRB measures is that its disintegration in relation to measurable partitions subordinate to unstable manifolds is absolutely continous with respect to the Lesbesgue measures in the same manifolds. This work follows the footsteps of Segert [16] in the study of the applicability of the non commutative integration theory of Alain Connes to the analysis of SRB measures for hyperbolic dynamical systems of the type (M, f) with M a compact manifold and f a 'C POT. 2' diffeomorphism. In this work the proof of Rokhlins disintegration theorem is presented using the concept of conditional expectation. An introduction to the theory of non commutative integration of Alain Connes is provided. Its shown the existence of a injection between SRB measures in hyperbolic dynamical systems and transverse measures defined on this system
 
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Gabriel_rev.pdf (1.80 Mbytes)
Publishing Date
2013-10-02
 
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