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Chaos and Turing machines on bidimensional models at zero temperature

Nosaki, Gregorio Luis Dalle Vedove

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística 2020-12-15

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  • Título:
    Chaos and Turing machines on bidimensional models at zero temperature
  • Autor: Nosaki, Gregorio Luis Dalle Vedove
  • Orientador: Proença, Rodrigo Bissacot; Thieullen, Philippe
  • Assuntos: Formalismo Termodinâmico; Medida De Equilíbrio; Subshift; Equilibrium Measure; Thermodynamic Formalism
  • Notas: Tese (Doutorado)
  • Descrição: In equilibrium statistical mechanics or thermodynamics formalism one of the main objectives is to describe the behavior of families of equilibrium measures for a potential parametrized by the inverse temperature beta. Here we consider equilibrium measures as the shift invariant measures that maximizes the pressure. Other constructions already prove the chaotic behavior of these measures when the system freezes. One of the most important examples was given by Chazottes and Hochman where they prove the non-convergence of the equilibrium measures for a locally constant potential when the dimension is bigger than or equal to 3. In this work we present a construction of a bidimensional example described by a finite alphabet and a locally constant potential in which there exists a subsequence where the non-convergence occurs for any sequence of equilibrium measures at inverse temperatures beta. In order to describe such an example, we use the construction described by Aubrun and Sablik which improves the result of Hochman used in the construction of Chazottes and Hochman.
  • DOI: 10.11606/T.45.2020.tde-04012021-102503
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Matemática e Estatística
  • Data de criação/publicação: 2020-12-15
  • Formato: Adobe PDF
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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