Uniform isochronous centers in planar polynomial differential systems of degree 5

• Grant number: 15/07612-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2016
• End date: December 18, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Jackson Itikawa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM
• Associated scholarship(s): 16/23285-9 - On the real Jacobian conjecture and the center-type singularities, BE.EP.PD

Abstract

In this project we aim to investigate the uniform isochronous centers in planar differential systems of degree 5. In particular, we want to study necessary and sufficient conditions to characterize such systems, to provide a classification of their global phase portraits in the Poincaré disc, and also to analyze the bifurcation of limit cycles when the uniform isochronous center is perturbed into the class of all polynomial differential systems of degree 5.

Scientific publications

(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)

ITIKAWA, JACKSON; LLIBRE, JAUME; NOVAES, DOUGLAS D.. A new result on averaging theory for a class of discontinuous planar differential systems with applications. REVISTA MATEMATICA IBEROAMERICANA, v. 33, n. 4, p. 1247-1265, 2017. (15/02517-6, 15/07612-7, 15/24841-0)

ITIKAWA, JACKSON; LLIBRE, JAUME; MEREU, ANA CRISTINA; OLIVEIRA, REGILENE. LIMIT CYCLES IN UNIFORM ISOCHRONOUS CENTERS OF DISCONTINUOUS DIFFERENTIAL SYSTEMS WITH FOUR ZONES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 22, n. 9, p. 3259-3272, NOV 2017. (12/18780-0, 15/07612-7, 14/00304-2)