Shadowing Lemma on Infinite Dimensional Dynamical Systems

• Grant number: 24/16879-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2025
• End date: April 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo José Dias Nascimento
• Grantee: Carlos Roberto Takaessu Junior
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 20/14075-6 - Dynamical systems and their attractors under perturbations, AP.TEM

Abstract

In this project we propose to study the well-known property of Shadowing in infinite-dimensional dynamical systems. Our main objective is to extend the following finite-dimensional result: every (continuous) Morse-Smale dynamical system defined on a compact manifold without border has the Lipschitz-Shadowing property. In fact, we want to extend this result to a neighborhood of a global attractor of a Morse-Smale dynamical system defined over an infinite-dimensional Banach space. We also want to study the non-autonomous Lambda Lemma in order to better understand the topological stability of Morse-Smale evolution processes.