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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.)

Lower bounds for the local cyclicity of centers using high order developments and parallelization

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Gouveia, Luiz F. S. [1, 2] ; Torregrosa, Joan [2]
Total Authors: 2
[1] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto - Brazil
[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia - Spain
Total Affiliations: 2
Document type: Journal article
Source: Journal of Differential Equations; v. 271, p. 447-479, JAN 15 2021.
Web of Science Citations: 1

We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. This technique is useful to study lower bounds for the local cyclicity of centers. We denote by M(n) the maximum number of limit cycles bifurcating from the origin via a degenerate Hopf bifurcation for a polynomial vector field of degree n. We get lower bounds for the local cyclicity of some known cubic centers and we prove that M(4) >= 20, M(5) >= 33, M(7) >= 61, M(8) >= 76, and M(9) >= 88. (C) 2020 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 20/04717-0 - Dynamical systems with symmetries and implicit differential equations
Grantee:Luiz Fernando da Silva Gouveia
Support Opportunities: Scholarships in Brazil - Post-Doctorate