Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres

Author(s)

Buzzi, Claudio A. ^[1] ; Rodero, Ana Livia ^[1] ; Torregrosa, Joan ^{[2, 3]}

Affiliation

^[1] Univ Estadual Paulista, UNESP, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

^[3] Ctr Recerca Matemat, Campus Bellaterra, Barcelona 08193 - Spain

• Document type: Journal article
• Source: JOURNAL OF NONLINEAR SCIENCE; v. 31, n. 6 DEC 2021.
• Web of Science Citations: 0

Abstract

The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify the centers of linear, quadratic homogeneous and a family of quadratic vector fields F subset of X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F. (AU)

• FAPESP's process: 17/08779-8 - Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds
• Grantee: Ana Livia Rodero
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/00440-7 - Study of limit cycles in piecewise smooth systems on the sphere
• Grantee: Ana Livia Rodero
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate