Web of Science: 10 citas, Scopus: 11 citas, Google Scholar: citas
Averaging methods of arbitrary order, periodic solutions and integrability
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Wu, Kesheng (Shanghai Jiao Tong University. Department of Mathematics)
Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)

Fecha: 2016
Resumen: In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential systems, and it unifies many different kinds of averaging methods. Applying our theory to autonomous analytic differential systems, we obtain some conditions on the existence of limit cycles and integrability. For polynomial differential systems with a singularity at the origin having a pair of pure imaginary eigenvalues, we prove that there always exists a positive number N such that if its first N averaging functions vanish, then all averaging functions vanish, and consequently there exists a neighborhood of the origin filled with periodic orbits. Consequently if all averaging functions vanish, the origin is a center for n = 2. Furthermore, in a punctured neighborhood of the origin, the system is C^ completely integrable for n > 2 provided that each periodic orbit has a trivial holonomy. Finally we develop an averaging theory for studying limit cycle bifurcations and the integrability of planar polynomial differential systems near a nilpotent monodromic singularity and some degenerate monodromic singularities.
Nota: Número d'acord de subvenció MICINN/MTM2011-22877
Nota: Número d'acord de subvenció AGAUR/2014/SGR–1204
Nota: Número d'acord de subvenció AGAUR/2014/SGR–568
Nota: Número d'acord de subvenció MINECO/MTM2013-40998-P
Nota: Número d'acord de subvenció EC/FP7/2012/316338
Nota: Número d'acord de subvenció EC/FP7/2012/316339
Nota: Agraïments: The third and fourth authors are partially supported by NNSF of China grant number 11271252, by RFDP of Higher Education of China grant number 20110073110054. The fourth author also is supported by the innovation program of Shanghai Municipal Education Commission grant 15ZZ012.
Derechos: Tots els drets reservats.
Lengua: Anglès.
Documento: article ; recerca ; submittedVersion
Materia: Averaging method ; Differential systems ; Integrability ; Limit cycle ; Polynomial differential systems
Publicado en: Journal of differential equations, Vol. 260 (2016) , p. 4130-4156, ISSN 0022-0396

DOI: 10.1016/j.jde.2015.11.005


Preprint
30 p, 812.6 KB

El registro aparece en las colecciones:
Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
Artículos > Artículos de investigación
Artículos > Artículos publicados

 Registro creado el 2017-01-23, última modificación el 2019-10-30



   Favorit i Compartir