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 |