不可积的Pfronian系统
Non-Integrable Pfaffian Systems
摘要：
本文讨论了一种递归几何方法，这种方法是由Élie Cartan和von Weber（[1]，[11]）提出的，它使我们能够逐步确定一个不一定可积也不一定正则的Pfronian系统的极大积分流形。当然，这种积分流形的尺寸可以从点到点变化，但更可以在给定点变化，这取决于它们的经常性构造的选择。当系统是正规的和可积的，那么，当然，我们得到的最大积分叶的积分叶理。注意力也给予那些可积系统，可以集成的quadratures这是，在19世纪，许多人的梦想。然而，我们的主要兴趣在于提高乔丹-Hölder积分过程，以构建当地最大的积分流形，找到许多应用。
英文摘要：
We discuss a recurrent geometrical method, due to Élie Cartan and von Weber ([1],[11]) enabling us to determine, step by step, the maximal integral manifolds of a not necessarily integrable nor regular Pfaffian system. The dimensions of such integral manifolds can, of course, vary from point to point but more so can vary at a given point it depending upon the choice of their recurrent buildup. When the system is regular and integrable then, of course, we obtain the maximal integral leaves of the integral foliation. Attention is also given to those integrable systems that can be integrated by quadratures which was, in the 19th century, the dream of many. However, our main interest resides in enhancing the Jordan-Hölder integration procedure so as to construct the local maximal integral manifolds that find many applications.
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