The Cauchy atlas on the manifold of all complete ODE solutions
Classical Analysis and ODEs
2007-05-23 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.math/0312317,
title = {The Cauchy atlas on the manifold of all complete ODE solutions},
author = {P. Chladek and L. Klapka},
journal= {arXiv preprint arXiv:math/0312317},
year = {2007}
}
Comments
6 pages, Latex