Introduction to dynamical systems and ergodic theory

• Grant number: 19/15373-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2019
• End date: July 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Edson de Faria
• Grantee: Bruno de Almeida Nussenzveig
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

Beginning with the qualitative study of ordinary differential equations of physical interest, Dynamical Systems now attract a great deal of interest by the global mathematical community. The field is in rapid development, as well as its applications, ranging from mathematical physics to number theory. However, despite its position of relevance in contemporary mathematics and its surprising accessibility in some cases it is rare for the budding mathematician to be to introduced to dynamical systems theory during his undergraduate studies. One case deserving attention is that of one-dimensional dynamical systems, some aspects of which can be understood as soon as the student acquires basic knowledge of functions of a single real or complex variable. Thus, the aim of this project is to initiate the student in his study of dynamical systems, with special focus given to one-dimensional dynamics. It is expected that, upon completion of this project, the student will become closer to the possibility of doing research on the subject and contributing to its future development.