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

Abstract

This project contemplates the study of the time of the solution curves for differential equationswhen 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.