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The Cauchy atlas on the manifold of all complete ODE solutions

P. Chladek·L. Klapka
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Abstract

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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P. Chladek, L. Klapka. 2003-12-16. The Cauchy atlas on the manifold of all complete ODE solutions. https://arxiv.org/abs/math/0312317

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