Continuous or piecewise smooth dynamical systems on 2 and 3 dimensional manifolds.

• Grant number: 23/04061-6
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2023
• End date: July 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cláudio Gomes Pessoa
• Grantee: Cláudio Gomes Pessoa
• 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
• City of the host institution: São José do Rio Preto

Abstract

The theory of dynamical systems is one of the most important tools in the qualitative and quantitative study of mathematical models of applied sciences. Most of these models are formulated using differential equations (continuous dynamic systems). Since the first works published by Poincaré at the end of the 19th century, the qualitative theory of differential equations has experienced a significant expansion. While old problems still persist, new techniques have been developed to solve many of them, as well as giving rise to new questions as intriguing and fascinating as the old ones. One of the most studied objects are vector fields defined by ordinary differential equations in the plane or on surfaces. However, these topics are far from being fully understood and there are still many problems to be solved, such as the 16th Hilbert problem, the Center-Focus problem, the Integrability problem, etc. This project aims to study the qualitative theory of ordinary differential equations in several lines of research. These involve:* Polynomial vector fields with two or more variables in two or three dimensional manifolds;* Global Dynamics of Quadratic Polynomial Vector Fields in R3;* Study of the Center-Focus problem in two-dimensional manifolds;* Discontinuous vector fields;* Piecewise linear vector fields. (AU)

Scientific publications

(4)

(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)

BRAGA, DENIS DE CARVALHO; DA FONSECA, ALEXANDER FERNANDES; MELLO, LUIS FERNANDO; RIBEIRO, RONISIO MOISES; PESSOA, CLAUDIO GOMES. Crossing Limit Cycles Bifurcating from Two or Three Period Annuli in Discontinuous Planar Piecewise Linear Hamiltonian Differential Systems with Three Zones. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 33, n. 10, p. 17-pg., 2023-08-01. (19/10269-3, 19/07316-0, 23/04061-6)

PESSOA, CLAUDIO; QUEIROZ, LUCAS. Formal integrability for monodromic nilpotent singular points in R3. BULLETIN DES SCIENCES MATHEMATIQUES, v. 200, p. 28-pg., 2025-02-26. (19/13040-7, 19/10269-3, 23/04061-6)

PESSOA, CLAUDIO; RIBEIRO, RONISIO; NOVAES, DOUGLAS; GOUVEIA, MARCIO; EUZEBIO, RODRIGO. On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one. NONLINEAR DYNAMICS, v. 111, n. 22, p. 23-pg., 2023-11-01. (22/04040-6, 18/13481-0, 19/10269-3, 23/04061-6, 22/09633-5)

PESSOA, CLAUDIO; RIBEIRO, RONISIO. Bifurcation of limit cycles from a periodic annulus formed by a center and two saddles in piecewise linear differential system with three zones. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 80, p. 17-pg., 2024-06-27. (19/10269-3, 23/04061-6)