A method of desingularization for analytic two-dimensional vector field families |
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Authors: | Zofia Denkowska Robert Roussarie |
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Affiliation: | (1) Jagellonian University invited at Université Paris Sud Mathématiques, bât. 425, 91 405 Orsay;(2) Laboratoire de Topologie Faculté Mirande, Université de Bourgogne, b.p. 138, 21 004 Dijon |
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Abstract: | 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. |
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