Per citar aquest document: http://ddd.uab.cat/record/145332
Scopus: 1 cites, Web of Science: 0 cites,
Vector fields with homogeneous nonlinearities and many limit cycles
Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2015
Resum: Consider planar real polynomial differential equations of the form x'=Lx X_n(x), where x=(x,y) R^2, L is a 2×2 matrix and X_n is a homogeneous vector field of degree n > 1. Most known results about these equations, valid for infinitely many n, deal with the case where the origin is a focus or a node and give either non-existence of limit cycles or upper bounds of one or two limit cycles surrounding the origin. In this paper we improve some of these results and moreover we show that for n 3 odd there are equations of this form having at least (n 1)/2 limit cycles surrounding the origin. Our results include cases where the origin is a focus, a node, a saddle or a nilpotent singularity. We also discuss a mechanism for the bifurcation of limit cycles from infinity.
Nota: Número d'acord de subvenció MCYT/MTM 2008-03437
Nota: Número d'acord de subvenció AGAUR/2014/SGR-410
Nota: Número d'acord de subvenció EC/FP7/2012/316338
Nota: Agraïments: The second author is partially supported by NNSF of China grant 11431008, NSF of Shanghai grant 15ZR1423700 and NSF of Jiangsu grant BK 20131285. The third author is partially supported by NNSF of China grant 11271252, by RFDP of Higher Education of China grant 20110073110054, by innovation program of Shanghai Municipal Education Commission grant 15ZZ012.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Limit cycles ; Nilpotent singularity ; Polynomial differential equations
Publicat a: Journal of Differential Equations, Vol. 258 (2015) , p. 3286-3303, ISSN 0022-0396

DOI: 10.1016/j.jde.2015.01.009


Preprint
19 p, 397.8 KB

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