Bifurcation of limit cycles from some uniform isochronous centers
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Makhlouf, Ammar

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.
Note: Número d'acord de subvenció MINECO/MTM2008-03437
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció EC/FP7/2012/318999
Note: Número d'acord de subvenció EC/FP7/2012/316338
Note: Agraïments: FEDER-UNAB-10-4E-378.
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; recerca ; preprint
Subject: Averaging theory ; Periodic solutions ; Uniform isochronous centers ; Weak Hilbert problem
Published in: Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis, Vol. 22 (2015) , p. 381-394, ISSN 1918-2538



Preprint
12 p, 390.4 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2016-01-12, last modified 2017-07-14



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