Shilnikov Connections in Discontinuous Foliations and Cocycles of Delayed Difference Equations

• Grant number: 25/01340-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2025
• End date: May 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Ricardo da Silva
• Grantee: Matheus Gonçalves Cassiano da Cunha
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 23/02959-5 - Non-Smooth Systems and Singular Perturbations, AP.R

Abstract

First, we will discuss properties of Shilnikov sliding connections in Filippov fields. We will analyze behavior in high dimensions, complexity (dimensionality) in variations of a parameter, and homotopic types of closed orbits.Second, we will discuss the relationship between hyperbolic cocycles and difference/differential equations with exponential dichotomy, as well as properties arising from this relationship and from certain applications, such as robustness and generalizations of the notion of spectrum of a linear operator.