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Open dynamical systems, beta expansions and symbolic dynamics

Grant number: 14/25679-9
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): June 01, 2015
Effective date (End): November 30, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal researcher:André Salles de Carvalho
Grantee:Rafael Alcaraz Barrera
Home 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)

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