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A characterization of isochronous centres in terms of symmetries
dc.contributor.author | Freire, Emilio |
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Guillamon Grabolosa, Antoni |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-04-30T07:52:51Z |
dc.date.available | 2007-04-30T07:52:51Z |
dc.date.created | 2000 |
dc.date.issued | 2000 |
dc.identifier.uri | http://hdl.handle.net/2117/800 |
dc.description.abstract | 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. |
dc.format.extent | 14 |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Dynamical systems |
dc.subject.lcsh | Differential equations |
dc.subject.other | isochronous centres |
dc.subject.other | quadratic-like Hamiltonian systems |
dc.subject.other | groups of symmetries |
dc.subject.other | normalizers |
dc.title | A characterization of isochronous centres in terms of symmetries |
dc.type | Article |
dc.subject.lemac | Equacions diferencials ordinàries |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::34 Ordinary differential equations::34C Qualitative theory |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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