Artículos de revistas
Lower bounds for the local cyclicity of centers using high order developments and parallelization
Fecha
2021-01-15Registro en:
Journal Of Differential Equations. San Diego: Academic Press Inc Elsevier Science, v. 271, p. 447-479, 2021.
0022-0396
10.1016/j.jde.2020.08.027
WOS:000596071000016
Autor
Univ Autonoma Barcelona
Universidade Estadual Paulista (Unesp)
Institución
Resumen
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.