Averaging theory for nonergodic Hamiltonian systems

• Grant number: 16/00357-4
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: August 01, 2016
• End date: September 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Hélcio Martinho Júnior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

In a series of recent works, the supervisor and colleagues found evidence that non-ergodicity of a chaotic Hamiltonian system universally leads to entropy growth and, consequently, the exponential growth of energy during a periodic oscillation parameters. In this project, we aim at building a rigorous mathematical theory to describe this phenomenon. This is an important step towards understanding the dynamics Hamiltonian. We will replace the theorem of Anosov-Kasuga by a general principle of averages that applies to any Hamiltonian system, not only the ergodic. (AU)