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Symbolic dynamics: an introduction through hyperbolic examples

Grant number: 15/16911-8
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2015
Effective date (End): September 30, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:José Régis Azevedo Varão Filho
Grantee:Pedro Griguol de Mattos
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This undergraduate research project is an introduction to Dynamical Systems through symbolic dynamics. The student will get in touch to the basic concepts of the area, he will study some of the main toy models such as Bernoulli Shifts (and subshifts), expansive endomorphism on the torus and the Smale Horseshoe. On a second part of the project the student has to understand the dynamics of these toy models by conjugating them with its symbolic dynamics. These themes are classic and involve different fields of mathematics.