LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
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非线性一阶偏微分方程的局部分类
DOI：
10.1070/rm1975v030n01abeh001402
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发表时间：
1975
影响因子：
0.9
通讯作者：
V. Lychagin
中科院分区：
文献类型：
--
作者：
V. Lychagin
第一章.第一节非线性一阶微分方程几何§ 1。Jets § 2.非线性微分方程与多值解§ 3.接触同态和对称§ 4。接触向量场的代数§ 5。柯西问题（Cauchy's Problem）6对合方程§ 7. Darboux和Chern定理第二章。常微分方程的局部分类§ 1。问题的陈述§ 2。正则方程的局部分类§ 3。正则对合方程的局部可解性第三章。一阶微分方程的奇异点§ 1。对合方程在奇点处的海森矩阵§ 2. CSP分类§ 3.第四章范式。方程在奇点处的形式分类§ 1.局部等价性和局部溶解度之间的联系§ 2。方程在奇点处的形式解§ 3. Hamilton算子局部分类的代数不可解性第五章奇点处的局部分类§ 1.充分条件§ 2.局部分类的偶数维Pfweian形式在附近的一个奇点§ 3。奇异点邻域内的Hamilton算子的局部分类参考文献
ContentsIntroduction Chapter I. Geometry of non-linear first order differential equations § 1. Jets § 2. Non-linear differential equations and many-valued solutions § 3. Contact diffeomorphisms and symmetries § 4. The algebra of contact vector fields § 5. Cauchy's problem § 6. Involutory equations § 7. The theorems of Darboux and Chern Chapter II. Local classifications of regular differential equations § 1. Statement of the problem § 2. Local classification of regular equations § 3. Local solubility of regular involutory equations Chapter III. Singular points of first order differential equations § 1. The Hessian of an involutory equation at a singular point § 2. CSp-classification § 3. Normal forms Chapter IV. Formal classification of equations at a singular point § 1. The connection between local equivalence and local solubility § 2. Formal solubility of equations at a singular point § 3. Algebraic insolubility of the local classification of Hamiltonians Chapter V. Local classification at a singular point § 1. Sufficient conditions § 2. Local classification of even-dimensional Pfaffian forms in the neighbourhood of a singular point § 3. Local classification of Hamiltonians in the neighbourhood of a singular point References