Sliding cycles of regularized piecewise smooth vector fields having higher order tangency points

• Grant number: 24/00392-0
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: April 30, 2024
• End date: April 29, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Otavio Henrique Perez
• Supervisor: Renato Huzak
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Hasselt University, Diepenbeek, Belgium
• Associated to the scholarship: 21/10198-9 - Invariant manifolds and limit periodic sets of discontinuous foliations, BP.PD

Abstract

The Sotomayor-Teixeira regularization is widely used in the study of theoretical and applied aspects of piecewise smooth vector fields. In addition, the study of different regularization processes, such as non-monotonic and non-linear regularizations, has attracted attention because it expands the possibilities of the dynamics of the associated slow-fast system. This research project aims to study slow-fast systems associated with linear and non-linear regularizations. We will use the Slow Divergence Integral to estimate the number of limit cycles of a vector field regularized according to Sotomayor-Teixeira, in the presence of a tangency point of any even order. We also propose to study the relationship between different regularization processes and the codimension of the singularities of the associated slow-fast systems.