Topological and analytical techniques for robustness and ergodicity of global dynamics

• Grant number: 22/03201-6
• Support Opportunities: Research Grants - Initial Project
• Start date: July 01, 2023
• End date: June 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Patricia Romano Cirilo
• Grantee: Patricia Romano Cirilo
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• City of the host institution: São José dos Campos
• Associated researchers: Ali Messaoudi ; Bryce Gollobit ; Enrique Ramiro Pujals ; Fábio Armando Tal ; Luciana Luna Anna Lomonaco ; Pedro Levit Kaufmann

Abstract

This Fapesp Pi Initial Project proposal intends to study topological and analytical aspects of global dynamical systems. We will mainly address the following topics: dynamics of linear operators in infinite-dimensional spaces; Mañé-Sad-Sullivan type arguments for stability and continuation of periodic orbits; transition to chaos: diffeomorphisms with positive entropy vs null entropy; dynamics of Lipschitzian operators. (AU)