The Cauchy atlas on the manifold of all complete ODE solutions

Details The Cauchy atlas on the manifold of all complete ODE solutions The Cauchy atlas on the manifold of all complete ODE solutions

2003-12-16

arxiv.org/abs/math/0312317v1

Mathematics

Classical Analysis and ODEs

6 pages, Latex

Scientific paper

In 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.

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