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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.