%0 Journal Article
%T The Cauchy atlas on the manifold of all complete ODE solutions
%A P. Chladek
%A L. Klapka
%J Mathematics
%D 2003
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0312317v1