Persistence of periodic solutions for higher order perturbed differential systems via Lyapunov-Schmidt reduction

• Grant number: 15/24841-0
• Support type: Scholarships abroad - Research Internship - Post-doctor
• Effective date (Start): February 01, 2016
• Effective date (End): April 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Marco Antônio Teixeira
• Grantee: Douglas Duarte Novaes
• Supervisor abroad: Jaume Llibre Salo
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Research place: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 15/02517-6 - Study of minimal sets in nonsmooth dynamical systems, BP.PD

Abstract

In order to understand the dynamics of a differential system, it is an imperative matter to establish conditions for the existence of invariant sets, such as periodic orbits. The problem of bifurcation of periodic solutions in differential systems can be often reduced to the problem of persistence of zeros of a certain function. So in this project we shall use the Lyapunov-Schmidt reduction to develop higher order bifurcation functions to control the persistence of zeros of some perturbed functions.

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)

LLIBRE, JAUME; NOVAES, DOUGLAS D.; RODRIGUES, CAMILA A. B. Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones. PHYSICA D-NONLINEAR PHENOMENA, v. 353, p. 1-10, SEP 1 2017. Web of Science Citations: 5.

NOVAES, DOUGLAS D.; TORREGROSA, JOAN. On extended Chebyshev systems with positive accuracy. Journal of Mathematical Analysis and Applications, v. 448, n. 1, p. 171-186, APR 1 2017. Web of Science Citations: 10.

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. Web of Science Citations: 4.