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Master's Dissertation
DOI
Document
Author
Full name
Bruno Hideki Fukushima Kimura
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Proença, Rodrigo Bissacot (President)
Cioletti, Leandro Martins
Iambartsev, Anatoli
Title in English
Gibbs measures on subshifts
Keywords in English
Equilibrium measures
Gibbs measures
Subshifts
Abstract in English
We study the properties of Gibbs measures for functions with d-summable variation defined on a subshift X. Based on Meyerovitch's work from 2013, we prove that if X is a subshift of finite type (SFT), then any equilibrium measure is also a Gibbs measure. Although the definition provided by Meyerovitch does not make any mention to conditional expectations, we show that in the case where X is a SFT it is possible to characterize these measures in terms of more familiar notions presented in the literature.
Title in Portuguese
Medidas de Gibbs em subshifts
Keywords in Portuguese
Medidas de equilíbrio
Medidas de Gibbs
Subshifts
Abstract in Portuguese
Nós estudamos as propriedades de medidas de Gibbs para funções com variação d-somável definidas em um subshift X. Baseado no trabalho de Meyerovitch de 2013, provamos que se X é um subshift de tipo finito (STF), então qualquer medida de equilíbrio é também uma medida de Gibbs. Embora a definição fornecida por Meyerovitch não faz qualquer menção à esperanças condicionais, mostramos que no caso em que X é um STF, é possível caracterizar estas medidas em termos de noções mais familiares apresentadas na literatura.
 
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Publishing Date
2019-07-04
 
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