engleski

Topological Equivalence of Planar Vector Fields and Their Generalised Principal Part

Let $\chi(R^2)$ be the space of $C^\infty$ planar vector fields. We consider the space $V\subset\chi(R^2)$ of vector fields with an isolated singularity and a fixed Newton diagram. We define the generalised principal part $X_{;\bar\Delta};$, using the Newton diagram. We prove that $X\in V$ is locally topologically equivalent to its minimal generalised principal part $X_{;\hat\Delta};$, if $X_{;\bar\Delta};$ is nondegenerate and X is not a monodromic vector field. In the proof we use the normal form method and the blowing-up method.

vector field ; singularity ; topological equivalence ; Newton diagram ; blowing-up

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