0000000000021890

AUTHOR

Zofia Denkowska

showing 2 related works from this author

A method of desingularization for analytic two-dimensional vector field families

1991

It is well known that isolated singularities of two dimensional analytic vector fields can be desingularized: after a finite number of blowing up operations we obtain a vector field that exhibits only elementary singularities. In the present paper we introduce a similar method to simplify the periodic limit sets of analytic families of vector fields. Although the method is applied here only to reduce to families in which the zero set has codimension at least two, we conjecture that it can be used in general. This is related to the famouss Hibert's problem about planar vector fields.

Vector calculus identitiesCurl (mathematics)Solenoidal vector fieldVector operatorGeneral MathematicsMathematical analysisFundamental vector fieldDirection vectorComplex lamellar vector fieldMathematicsVector potentialBoletim da Sociedade Brasileira de Matem�tica
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The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Connected componentDiscrete mathematicsSocial connectednessApplied Mathematics010102 general mathematicsDimension (graph theory)Mathematics::General Topology16. Peace & justiceKuratowski convergencesubanalytic sets01 natural sciencesKuratowski's theoremKuratowski convergence010101 applied mathematicsDefinable setMathematics::Logictame geometry0101 mathematicsLimit set[MATH]Mathematics [math]Kuratowski closure axiomsAnalysisMathematics
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