6533b82afe1ef96bd128b6ea
RESEARCH PRODUCT
A method of desingularization for analytic two-dimensional vector field families
Zofia DenkowskaRobert Roussariesubject
Vector calculus identitiesCurl (mathematics)Solenoidal vector fieldVector operatorGeneral MathematicsMathematical analysisFundamental vector fieldDirection vectorComplex lamellar vector fieldMathematicsVector potentialdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1991-03-01 | Boletim da Sociedade Brasileira de Matem�tica |