Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles

• Grant number: 20/06708-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2021
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Ricardo da Silva
• Grantee: Gabriel Alexis Rondón Vielma
• 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: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM
• Associated scholarship(s): 22/12123-9 - Piecewise holomorphic systems and regularization of Filippov systems, BE.EP.PD

Abstract

We will study the behavior of the orbits of the regularized systems around tangential degenerate singularities using the techniques of geometric theory of singular perturbations.We will investigate the regularization of tangential polycycles for Filippov systems.We will also study piecewise Holomorphic systems.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GOUVEIA, LUIZ F. S.; DA SILVA, PAULO R. R.; RONDON, GABRIEL. Global Phase Portrait and Local Integrability of Holomorphic Systems. Qualitative Theory of Dynamical Systems, v. 22, n. 1, p. 26-pg., 2023-03-01. (20/06708-9, 19/10269-3, 20/04717-0)

NOVAES, DOUGLAS D.; RONDON, GABRIEL. On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities. PHYSICA D-NONLINEAR PHENOMENA, v. 442, p. 15-pg., 2022-10-01. (19/10269-3, 20/06708-9, 18/13481-0)

PEREZ, OTAVIO HENRIQUE; RONDON, GABRIEL; DA SILVA, PAULO RICARDO. Slow-Fast Normal Forms Arising from Piecewise Smooth Vector Fields. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. N/A, p. 18-pg., 2023-07-17. (21/10198-9, 19/10269-3, 22/12123-9, 20/06708-9, 16/22310-0)

NOVAES, DOUGLAS D.; RONDON, GABRIEL. Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles. Nonlinearity, v. 34, n. 6, p. 4202-4263, JUN 2021. (18/16430-8, 19/10269-3, 20/06708-9, 18/13481-0)

GOUVEIA, LUIZ F. S.; RONDON, GABRIEL; SILVA, PAULO R. DA. Piecewise holomorphic systems. Journal of Differential Equations, v. 332, p. 33-pg., 2022-09-25. (20/04717-0, 20/06708-9, 19/10269-3)