Topological equivalence of planar vector fields and their generalised principal part

[摘要] Let X(R-2) be the space of C-infinity planar vector fields. We consider the space V subset of X(R-2) of vector fields with an isolated singularity and a fixed Newton diagram. We define the generalised principal part X-<()over bar> of the vector field X is an element of V and give the nondegeneracy condition on X-<()over bar>, using the Newton diagram. We prove that X is an element of V is locally topologically equivalent to its minimal generalised principal part X-<()over cap>, if X-<()over bar> is nondegenerate and X is not a monodromic vector held. In the proof we use the normal form method and the blowing-up method. (C) 2000 Academic Press.

[发布日期] 2000-10-10

[关键词] vector field;singularity;topological equivalence;Newton diagram;blowing-up