Ergodic theory and dynamic on homogeneous spaces

• Grant number: 16/22585-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2017
• End date: December 31, 2017
• 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 project is an introduction to ergodic theory and dynamics in homogeneous spaces. The student will study the basics of ergodic theory, such as ergodicity, ergodic theorem of Birkhoff, ergodic hierarchies, invariant measures, existence of invariant measures, hyperbolic plane of Poincaré, geodesic flow, horociclo flow and Fuchsianos groups. (AU)