非线性常微分方程的广义Wilczynski不变量
Generalized Wilczynski invariants for non-linear ordinary differential equations
摘要：
我们表明，经典的Wilczynski-Seashi不变量的线性系的常微分方程推广在一个自然的方式接触不变量的非线性常微分方程。我们探讨了与具有消失的广义Wilczynski不变量的方程相关联的几何结构，并建立了此类方程与复代数曲面上有理曲线的变形理论之间的关系。
英文摘要：
We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations that have vanishing generalized Wilczynski invariants and establish relationship of such equations with deformation theory of rational curves on complex algebraic surfaces.
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