The Cauchy atlas on the manifold of all complete ODE solutions

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dc.creatorChladek, P.
dc.creatorKlapka, L.
dc.date2003-12-16
dc.date.accessioned2026-07-07T05:03:58Z
dc.date.available2026-07-07T05:03:58Z
dc.descriptionIn this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete solution of some differentiable first-order ordinary differential equation on the initial Cauchy condition are deduced. The result is obtained by studying the Cauchy atlas on a manifold of complete solutions. The proof is constructive - the corresponding differential equation is obtained. The autonomous case and the linear case are discussed. The relation to the Sincov functional equation is clarified.
dc.description6 pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0312317
dc.identifierhttp://arxiv.org/abs/math/0312317
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69623
dc.subjectClassical Analysis and ODEs
dc.subjectDynamical Systems
dc.subject34C30; 34A12
dc.titleThe Cauchy atlas on the manifold of all complete ODE solutions
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