Introduction to Aubry-Mather theory

• Grant number: 06/01007-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2006
• End date: May 31, 2007
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Sergio Henrique Monari Soares
• Grantee: Júlio Frederico Hruza Alquéres
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project is related to a new development in the calculus of variations which is called Aubry-Mather Theory. Although the theories of Aubry and Mather have different motivations, they are closely related and have the mathematical foundation. We will not follow those approaches but will make a connection to classical results of the calculus of variations. From an introduction to the calculus of variations, the student will be leaded to modern dynamical systems theory. Moreover, some differential geometry applications will be discussed.