Open dynamical systems, beta expansions and symbolic dynamics

• Grant number: 14/25679-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): June 01, 2015
• Effective date (End): November 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: André Salles de Carvalho
• Grantee: Rafael Alcaraz Barrera
• 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 project is focused on the study of the topological and ergodic properties of open dynamical systems. In particular, we will work towards understanding properties such as transitivity, the specification property and intrinsic ergodicity for the family of mapsnx mod 1 for n greater or equal than 3 when a hole consisting on n-1 components is introduced. Also, we are interested in describe the mentioned properties for the Fibonnacci automorphism on the two dimensional torus T2 when an open connected set is removed and we want to provide a full description of the connections between the mentioned families of open dynamical systems and the theory of beta expansions. For these purposes, we will study the properties of lexicographic world of size n using inmax and minimax sequences. (AU)