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.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

AZEVEDO, VINICIUS TAVARES; LOPEZ-LAZARO, HERACLIO; TAKAESSU JUNIOR, CARLOS R.. Existence and continuity of pullback exponential attractors for a family of non-classical reaction-diffusion equations. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 152, p. 12-pg., 2026-01-01. (21/01931-4, 22/02172-2, 24/16879-6, 24/12782-8, 20/14353-6, 22/13001-4)