Set-oriented rigorous topological-numerical approach to the analysis of chaotic Itinerancy

• Grant number: 11/19378-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: January 27, 2012
• End date: February 22, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Visiting researcher: Pawel Pilarczyk
• Visiting researcher institution: Universidade do Minho (UMinho), Portugal
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The aim of this research project is to apply topological methods, based on the Conley Index, to the analysis of chaotic itinerancy. The main idea of this approach is to analyse the internal structure of a large isolating neighborhood with transitive and mixing dynamics, as seen at a finite resolution level by means of constructing small isolating neighborhoods arising from sets that exhibit short-term recurrent behavior, and then investigating connections between such neighborhoods. (AU)