Wada property in doubly transient chaos

• Grant number: 18/16728-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2018
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Rafael Ribeiro Dias Vilela de Oliveira
• Grantee: Carlo Domenico Longo de Lemos
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

Dissipative dynamical systems with three or more attractors and displaying transient chaos often exhibit the Wada property. In this case, each point belonging to the boundary between two basins of attraction necessarily belongs to the boundary of all the basins of the system. The Wada property is not merely an exotic geometric property. Rather, it has deep consequences for the dynamics since it increases the uncertainty about the asymptotic state to be approached. In this project, we propose the study of the Wada property in systems which exhibit Doubly Transient Chaos, a recently introduced concept which describes the behavior of dissipative systems under no energy reinjection. We aim at leading the student to learn both (I) advanced topics in topology such as the one of indecomposable continuum and (II) numerical techniques of widespread use in Physics and Applied Math, as well as (III) fostering the student's ability to perform research in a recent and important area.