Dmitry Turaev | Imperial College London - Inglaterra

• Grant number: 15/50417-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 25, 2016
• End date: October 19, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: CONFAP ; Newton Fund, with FAPESP as a partner institution in Brazil
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Tiago Pereira da Silva
• Visiting researcher: Dmitry Turaev
• Visiting researcher institution: Imperial College London, England
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In a series of recent works, we and our collaborators gave empiric and numerical evidence that the non-ergodicity of a chaotic Hamiltonian system must universally lead to the sustained growth of the entropy of the system and, as a consequence, to the exponential growth of energy at a slow periodic oscillation of parameters. The goal of the project is to build a mathematically rigorous theory of this phenomenon. The result will be an important step towards the understanding of Hamiltonian dynamics. We will replace the Anosov-Kasuga theorem by a general averaging principle which is applicable to all Hamiltonian systems, not only ergodic ones. (AU)