Symbolic dynamics: an introduction through hyperbolic examples

• Grant number: 15/16911-8
• Support Opportunities: 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 Investigator: José Régis Azevedo Varão Filho
• Grantee: Pedro Griguol de Mattos
• Host 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.