完全ODE解流形上的Cauchy图集
The Cauchy atlas on the manifold of all complete ODE solutions
摘要：
本文给出了一类一阶可微常微分方程的完全解依赖于初值柯西条件的映射的充要条件。通过研究完备解流形上的柯西图集得到了这个结果。证明是建设性的-相应的微分方程得到。自治的情况下，线性的情况进行了讨论。阐明了与Sincov函数方程的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
