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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Limit cycles for some families of smooth and non-smooth planar systems

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Buzzi, Claudio A. [1] ; Romano Carvalho, Yagor [1] ; Gasull, Armengol [2, 3]
Total Authors: 3
[1] Univ Estadual Paulista, Math Dept, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, Edif Cc, E-08193 Barcelona - Spain
[3] Ctr Recerca Matemat, Edif Cc, Campus Bellaterra, Barcelona 08193 - Spain
Total Affiliations: 3
Document type: Journal article
Web of Science Citations: 0

We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be applied to models where the smoothness is lost on the set Sigma = [xy = 0]. They also motivate to consider a variant of Hilbert 16th problem, where the goal is to bound the number of limit cycles in terms of the number of monomials of a family of polynomial vector fields, instead of doing this in terms of their degrees. (C) 2021 Elsevier Ltd. All rights reserved. (AU)

FAPESP's process: 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 18/05098-2 - Study of limit cycles in piecewise smooth systems on the cylinder
Grantee:Yagor Romano Carvalho
Support Opportunities: Scholarships abroad - Research Internship - 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