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Center conditions for a class of planar rigid polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rabanal, Roland (Pontificia Universidad Católica del Perú. Departamento de Ciencias)

Data: 2015
Resum: In general the center–focus problem cannot be solved, but in the case that the singularity has purely imaginary eigenvalues there are algorithms to solving it. The present paper implements one of these algorithms for the polynomial differential systems of the form x = −y + xf (x)g(y), y = x + yf (x)g(y), where f (x) and g(y) are arbitrary polynomials. These differential systems have constant angular speed and are also called rigid systems. More precisely, this paper gives focal bases of these systems, and then necessary and sufficient conditions in order to have an uniform isochronous center. In particular, the existence of a focus with the highest order is also studied.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Focal basis ; Isochronous center ; Limit cycles ; Lyapunov quantities ; The center problem
Publicat a: Discrete and Continuous Dynamical Systems. Series A, Vol. 35 Núm. 3 (2015) , p. 1075-1090, ISSN 1553-5231

DOI: 10.3934/dcds.2015.35.1075

18 p, 697.9 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Articles > Articles de recerca
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