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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Differential Equations
( Vol. 167 NO.1 / (2000))
Topological Equivalence of Planar Vector Fields and Their Generalised Principla Part
Vesna Zupanovic,
Pages. 1-15
Abstract Let $mathfrak X(R^2)$ be the space of $C^infty$ planar vector fields. We consider the space
$V subset mathfrak X(R^2)$ of vector fields with an isolated singularity and a fixed Newton diagram.
We define the generalised principal part $X_{ar Delta}$ of the vector field $X in V$ and give the
nondegeneracy condition on $X_{ar Delta}$, using the Newton diagram. We prove that $X in V$
is locally topologically equivalent to its minimal generalised principal part $X_{hat Delta}$, if $X_{ar Delta}$
is nondegenerate and $X$ is is not a monodromic vector field. In the proof we use the
normal form method and the blowing-up method.
Contents 1. Introduction
2. Generalised principal part
Key words vector field, singularity, topological equivalence, Newton diagram, blowing-up
Mathmatical Subject Classification