Local compactification to countable Markov shifts

• Ano de defesa: 2022
• Autor(a) principal: Rocha, Henrique Corsini Soares
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Conformal measures; Dinâmica simbólica; Dynamical systems; Medidas conformes; Sistemas dinâmicos; Symbolic dynamics
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-06012023-195534/

Around twenty year ago Ruy Exel and Marcelo Laca first discovered the so-called Exel- Laca algebras which are an attempt to extend Cuntz-Krieger algebras to infinite matrices. From the point of view of the theory of countable Markov shifts, these algebras are interesting because they contain some commutative sub-algebras whose spectrum is a local compactification, or compactification depending on the matrix associated to the countable Markov shift, of a countable Markov which is not locally compact. Furthermore, such construction leaves invariant Markov shifts which are already compact and it does not depend on anything other than the matrix describing the Markov shift. The objective of this work is to describe in detail such local compactifications to those that are very knowledgeable on the theory of C*-alegbras and to define some basic notion such as conformal measures to such spaces.