A characterization of isochronous centres in terms of symmetries.

Título inglés	A characterization of isochronous centres in terms of symmetries.
Título español	Una caracterización de los centros isócronos en términos de simetrías.
Autor/es	Freire, Emilio ; Gasull, Armengol, Guillamon, Antoni
Organización	ESIC Univ. Sevilla, Sevilla, España;Dep. Nat. Univ. Auton. Barcelona, Barcelona, España;Dep. Mat. Apl. I Univ. Politec. Catalunya, Barcelona, España
Revista	0213-2230
Publicación	2004, 20(1): 205-222, 17 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity; this point of view forces a deeper insight into the potential and quadratic-like Hamiltonian systems. For these families we provide new ways to find isochronous centres, alternative to those already known from the literature.
Clasificación UNESCO	120219
Palabras clave español	Campos vectoriales ; Sistema hamiltoniano ; Período orbital ; Grupos de simetría ; Sistemas dinámicos
Código MathReviews	MR2076778
Código Z-Math	Zbl 1087.34010
Acceso al artículo completo