Large deviations principles for Gibbs-Equilibrium measures on countable Markov shifts at zero temperature

• Grant number: 12/06368-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2012
• End date: January 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Rodrigo Bissacot Proença
• Grantee: Edgardo Enrique Perez Reyes
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

The main problem in Ergodic Optimization it is the study of the maximizing measures: existence, support and their properties and the relationship of these measures which other mathematical branches. Among the usual approaches we have to point out the limit of Gibbs Measures when the temperature goes to zero in systems where the potential function has some regularity, sub-actions and the study via periodic orbits of the system. The project for this PhD is to study such problems in the non-compact setting and to obtain large deviation principles. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

REYES, Edgardo Enrique Perez. Large deviation principle for Gibbs-equilibrium states on contable shifts at zero temperature.. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.