Metric Coordinate Systems

Details Metric Coordinate Systems Metric Coordinate Systems

2002-06-24

arxiv.org/abs/math/0206253v1

Mathematics

Dynamical Systems

31 pages, 2 figures

Scientific paper

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.

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