Non commutative integration theory and hyperbolic dynamic

Author(s)

Gabriel Elias Mantovani

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2013-08-20

Examining board members

Ali Tahzibi; Alexandre Tavares Baraviera; José Régis Azevedo Varão Filho

• Advisor: Ali Tahzibi

Abstract

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 (AU)

• FAPESP's process: 11/05426-0 - Noncommutative integration theory and hyperbolic dynamics
• Grantee: Gabriel Elias Mantovani
• Support Opportunities: Scholarships in Brazil - Master