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 Títol: A characterization of isochronous centres in terms of symmetries Autor: Freire, Emilio; Gasull Embid, Armengol; Guillamon Grabolosa, Antoni Data: 2000 Tipus de document: Article Resum: 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., $[X,U]=\mu X$, where $\mu$ is a scalar function), we provide a necessary and sufficient isochronicity condition based on $\mu$. 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. URI: http://hdl.handle.net/2117/800 Apareix a les col·leccions: EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions. Articles de revistaDepartaments de Matemàtica Aplicada. Articles de revista Comparteix: