Search results for "Vector calculus identities"

showing 2 items of 2 documents

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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Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields

2005

We study to what extent the known results concerning the behaviour of Hopf vector fields, with respect to volume, energy and generalized energy functionals, on the round sphere are still valid for the metrics obtained by performing the canonical variation of the Hopf fibration.

Curl (mathematics)Vector calculus identitiesSolenoidal vector fieldUnit vectorGeneral MathematicsMathematical analysisFundamental vector fieldVector fieldComplex lamellar vector fieldMathematicsVector potentialProceedings of the Royal Society of Edinburgh: Section A Mathematics
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