Symmetry, singularities and integrability in complex dynamics II: Rescaling and time-translation in two-dimensional systems

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The explicit integrability of second order ordinary differential equations invariant under time-translation and rescaling is investigated. Quadratic systems generated from the linearisable version of this class of equations are analysed to determine therelationship between the Painlevé and singularity properties of the different systems. The transformation contains a parameter and for critical values, intimately related to the possession of the Painlevé Property in the parent second order equation, one finds a difference from the generic behaviour. This study is a prelude to a full discussion of the class of transformations which preserve the Painlevé Property in the construction of quadratic systems from scalar nonlinear odes invariant under time translation and rescaling.
25 pp, latex. To appear in J.Math.Anal.Appl

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Exactly Solvable and Integrable Systems, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/79891

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0011002
 http://arxiv.org/abs/nlin/0011002

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arXiv