Home > Articles > Published articles > Bifurcation of limit cycles from some uniform isochronous centers |
Date: | 2015 |
Abstract: | This article concerns with the weak 16-th Hilbert problem. More precisely, we consider the uniform isochronous centers x'=-y x^(n-1) y, y'= x x^(n-2) y^2 , for n = 2, 3, 4, and we perturb them by all homogeneous polynomial of degree 2, 3, 4, respectively. Using averaging theory of first order we prove that the maximum number N (n) of limit cycles that can bifurcate from the periodic orbits of the centers for n = 2, 3, under the mentioned perturbations, is 2. We prove that N (4) 2, but there is numerical evidence that N (4) = 2. Finally we conjecture that using averaging theory of first order N (n) = 2 for all n > 1. Some computations have been made with the help of an algebraic manipulator as mathematica. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 318999 European Commission 316338 |
Note: | Agraïments: FEDER-UNAB-10-4E-378. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Averaging theory ; Periodic solutions ; Uniform isochronous centers ; Weak Hilbert problem |
Published in: | Dynamics of Continuous, Discrete and Impulsive Systems. Series A. Mathematical Analysis, Vol. 22, Num. 5 (2015) , p. 381-394, ISSN 1201-3390 |
Postprint 12 p, 390.4 KB |