论文标题
一阶微分方程的全球对称组和全球纠正定理
The global symmetry group of first order differential equations and the global rectification theorem
论文作者
论文摘要
对称分析可以提供适当的变量更改，即以几何术语，一种合适的差异性，可以简化给定方向场，这可以显着解决或研究微分方程。粗略地说，这是所谓的纠正定理。该结果的本地版本是普通微分方程领域中众所周知的定理。在本说明中，当方程满足Lipschitz状态时，我们证明了全球对应物。然后，我们使用此结果来确定这种普通微分方程的全局对称组。事实证明，假设Lipschitz条件，完整的对称组是两个差异组的平滑花环产物，并且完全不取决于方程式的形式。
Symmetry analysis can provide a suitable change of variables, i.e., in geometric terms, a suitable diffeomorphism that simplifies the given direction field, which can help significantly in solving or studying differential equations. Roughly speaking this is the so-called rectification theorem. The local version of this result is a well-known theorem in the field of ordinary differential equations. In this note we prove a global counterpart when the equation fulfils the Lipschitz condition. Then we use this result to determine the global symmetry group of such an ordinary differential equation. It turns out that, assuming the Lipschitz condition, the full symmetry group is a smooth wreath product of two diffeomorphism groups, and does not depend on the form of the equation, at all.
