Centers and limit cycles of vector fields defined on invariant spheres
Buzzi, Claudio (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)
Rodero, Ana Livia (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
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⊂ X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Vector fields on invariant spheres ; Integrability ; Center-focus problem ; Local cyclicity
Published in:	Journal of Nonlinear Science, Vol. 31, Issue 6 (December 2021) , art. 92, ISSN 1432-1467

DOI: 10.1007/s00332-021-09751-z

Postprint 24 p, 407.3 KB

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