The theory of Legendrian unfoldings and first-order differential equations
The theory of Legendrian unfoldings and first-order differential equations
复制标题
勒让德展开理论和一阶微分方程
DOI：
10.1017/s0308210500025865
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
S. Izumiya
中科院分区：
文献类型：
--
作者：
S. Izumiya
摘要我们考虑实值函数完全可积的一阶微分方程的一些性质。为了研究这一问题，我们引入了勒让德开折理论。我们给出了具有经典完全解的方程的勒让德开折的一个特征，并断言具有奇异解的方程组是完全可积方程空间中的开集，即使这样的开集在所有方程的空间中是稀疏的.
Synopsis We consider some properties of completely integrable first-order differential equations for real-valued functions. In order to study this subject, we introduce the theory of Legendrian unfoldings. We give a characterisation of equations with classical complete solutions in terms of Legendrian unfoldings, and also assert that the set of equations with singular solutions is an open set in the space of completely integrable equations even though such a set is thin in the space of all equations.