Abstract The Poincare compactification is an extension of a polynomial vector field to a compact manifold. We generalize this construction to weight-homogeneous vector fields with weight exponent ( 1 , l ) and different weight-degrees. Then we apply the new method to obtain some new information about the infinite singular points and in particular for Hamiltonian systems under generic conditions.

中文翻译：

---

具有权重度 (1,ℓ) 的权齐次多项式的 Poincaré 紧化的推广

摘要 Poincare 紧化是多项式向量场到紧流形的扩展。我们将这种构造推广到具有权重指数 ( 1 , l ) 和不同权重度的权重齐次向量场。然后我们应用新方法来获得关于无限奇异点的一些新信息，特别是对于通用条件下的哈密顿系统。