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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2007.tde-08052007-135433
Document
Author
Full name
Amanda de Lima
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2007
Supervisor
Committee
Brandão, Daniel Smania (President)
Lopes, Artur Oscar
Tahzibi, Ali
Title in Portuguese
Cohomologia e propriedades estocásticas de transformações expansoras e observáveis lipschitzianos
Keywords in Portuguese
Cohomologia
Teorema do limite central
Transformações expansaroras
Variação limitada
Abstract in Portuguese
Provamos o Teorema do Limite Central para transformações expansoras por pedaços em um intervalo e observáveis com variação limitada. Utilizamos a abordagem desenvolvida por R. Rousseau-Egele, como apresentada por A. Broise. O método da demonstração se baseia no estudo de pertubações do operador de transferência de Ruelle-Perron-Frobenius. Uma contribuição original é dada no último capítulo, onde provamos que, para transformações markovianas expansoras, todos os observáveis não constantes, contínuos e com variação limitada não são infinitamente cohomólogos à zero, generalizando um resultado de Bamón, Rivera-Letelier, Urzúa and Kiwi para observáveis lipschitzianos e transformações 'z POT. n' . A demonstração se baseia na teoria dos operadores de Ruelle-Perron-Frobenius desenvolvida nos capítulos anteriores
Title in English
Cohomology and stochastics properties of expanding maps and lipschitzians observables
Keywords in English
Bounded variation
Central Limit Theorem
Cohomology
Expanding maps
Abstract in English
We prove the Central Limit Theorem for piecewise expanding interval transformations and observables with bounded variation, using the approach of J.Rousseau-Egele as described by A. Broise. This approach makes use of pertubations of the so-called Ruelle-Perron-Frobenius transfer operator. An original contribution is given in the last chapter, where we prove that for Markovian expanding interval maps all observables which are non constant, continuous and have bounded variation are not infinitely cohomologous with zero, generalizing a result by Bamón, Rivera-Letelier, Urzúa and Kiwi for Lipschitzian observables and the transformations 'z POT. n' . Our demosntration uses the theory of Ruelle-Perron-Frobenius operators developed in the previos chapters
 
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Publishing Date
2007-05-08
 
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