Gradient Semigroups under perturbation and cascade systems.

• Grant number: 25/04648-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Erick Rodrigues Canterle
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 20/14075-6 - Dynamical systems and their attractors under perturbations, AP.TEM

Abstract

The final goal of the project is to show that cascade systems are gradients. This project will be divided into:1. Show that the notions of gradient and dynamically gradient semigroups are equivalent;2. Study the qualitative properties of attractors of autonomous and non-autonomous dynamical systems;3. Use the notion of dynamically gradient semigroups for non-autonomous dynamical systems to study the behavior of such a structure under perturbations;4. Show that cascade systems are dynamically gradients and use the skew-product formulation to show that they are stable under non-autonomous perturbations. (AU)