Study of limit cycles in piecewise smooth systems on the cylinder

• Grant number: 18/05098-2
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2018
• End date: July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Yagor Romano Carvalho
• Supervisor: Armengol Gasull
• 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
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization, BP.DR

Abstract

Study aiming to obtain lower bound for the number of limit cycles for a special class of Ordinary Differential Equations piecewise smooth and defined in the cylinder. The main tool to be used is the Melnikov Theory. In a second moment, we analyze the regularization of such piecewise smooth systems by looking for smooth approximations that have the same amount of limiting cycles and which approximate uniformly the initial system.

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)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; GASULL, ARMENGOL. The local period function for Hamiltonian systems with applications. Journal of Differential Equations, v. 280, p. 590-617, APR 15 2021. (19/10269-3, 16/00242-2, 18/05098-2)

BUZZI, CLAUDIO A.; ROMANO CARVALHO, YAGOR; GASULL, ARMENGOL. Limit cycles for some families of smooth and non-smooth planar systems. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 207, JUN 2021. (16/00242-2, 18/05098-2, 19/10269-3)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; LLIBRE, JAUME. Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 37, n. 4, p. 19-pg., 2022-09-28. (21/14695-7, 16/00242-2, 19/10269-3, 18/05098-2)