✦ LIBER ✦
Topological Equivalence of Planar Vector Fields and Their Generalised Principal Part
✍ Scribed by Vesna Županović
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 185 KB
- Volume
- 167
- Category
- Article
- ISSN
- 0022-0396
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✦ Synopsis
Let X(R 2 ) be the space of C planar vector fields. We consider the space V/X(R 2 ) of vector fields with an isolated singularity and a fixed Newton diagram. We define the generalised principal part X 2 of the vector field X # V and give the nondegeneracy condition on X 2 , using the Newton diagram. We prove that X # V is locally topologically equivalent to its minimal generalised principal part X 2 , if X 2 is nondegenerate and X is not a monodromic vector field. In the proof we use the normal form method and the blowing-up method.