Metric Coordinate Systems

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Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invoked to prove the analogue of the classical Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized space. A metric space version of Nagumo's Theorem is one consequence. Examples are given throughout.
31 pages, 2 figures

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Dynamical Systems, Metric Geometry, 37C10, 34G99 (Primary) 54E45 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/64383

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206253
 http://arxiv.org/abs/math/0206253

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arXiv