Limit cycles of linear vector fields on (S2)m ×Rn
Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2023
Abstract:	It is well known that linear vector fields defined in Rn cannot have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form (S2)m × Rn when such vector fields are perturbed inside the class of all linear vector fields. The study is done using averaging theory. We also present an open problem about the maximum number of limit cycles of linear vector fields on (S2)m × Rn.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación BES-2017-081570 European Commission 777911
Note:	This work was supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants PID2019-104658GB-I00 and BES-2017-081570, and the H2020 European Research Council grant MSCA-RISE-2017-777911. MSC2020: 34A30, 34C25, 34C29. Keywords: limit cycle, periodic orbit, isochronous center, averaging method.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Limit cycle ; Periodic orbit ; Isochronous center ; Averaging method
Published in:	Pacific Journal of Mathematics, Vol. 324, Issue 2 (June 2023) , p. 249-263, ISSN 1945-5844

DOI: 10.2140/pjm.2023.324.249

18 p, 334.8 KB

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