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Foliations and ergodicity of transverse measures

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Pedro Griguol de Mattos
Total Authors: 1
Document type: Master's Dissertation
Press: Campinas, SP.
Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:
Examining board members:
José Régis Azevedo Varão Filho; Eduardo Garibaldi; Fernando Nera Lenarduzzi
Advisor: José Régis Azevedo Varão Filho

This master's thesis is a study of the article "Unique ergodicity for horocycle foliations", by Rufus Bowen and Brian Marcus. The objective is to present the construction of invariant measures of the stable and unstable foliations of basic sets of Axiom A diffeomorphism. We show that these measures are unique in a certain sense, and for that we make use of a conjugacy to a symbolic space and a shift dynamics to translate the problem to something more manageable. The conjugacy exists thanks to the existence of Markov partitions (AU)

FAPESP's process: 18/02616-2 - Foliations and ergodicity of transverse measures
Grantee:Pedro Griguol de Mattos
Support Opportunities: Scholarships in Brazil - Master