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Bifurcation phenomena in time of differential equations

Grant number: 21/14450-4
Support Opportunities:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): September 01, 2022
Effective date (End): August 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Cláudio Gomes Pessoa
Grantee:Lucas Queiroz Arakaki
Supervisor: Jordi Villadelprat
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
Research place: Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:19/13040-7 - Nilpotent centers on the center manifolds, BP.DR


This project contemplates the study of the time of the solution curves for differential equations when distinct types of bifurcations occur, focusing in three topics: the study of the period of limit-cycles generated by non-elementary bifurcations, the time delay associated to the bottleneck or ghost phenomenom and the improvement of tools to obtain uniform developments of the period function for the cases in which the topology of a given polycycle is altered. The questions involved in this study are deeply related to the 16th Hilbert's problem and its weaker versions. (AU)

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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)
GOUVEIA, LUIZ F. S.; QUEIROZ, LUCAS. Lower bounds for the cyclicity of centers of quadratic three-dimensional systems. Journal of Mathematical Analysis and Applications, v. 530, n. 1, p. 16-pg., . (22/03801-3, 20/04717-0, 19/13040-7, 21/14450-4)

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