Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3242
Title: Singular perturbations arising in Hilbert's 16th problem for quadratic vector fields
Authors: SMITS, Bert
Issue Date: 1998
Publisher: WILEY-V C H VERLAG GMBH
Source: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 78(2). p. 133-136
Abstract: A solution to the second part of Hilbert's 16th problem consists of finding out (or proving the existence of) an upper bound to the number of limit cycles in the family of polynomial planar vector fields. In this article, we indicate a way to tackle the singular perturbation problems that have to be studied in the quadratic case. In particular, for perturbations from the family (lambda x - y)(x + 1) partial derivative/partial derivative + (x + lambda y)(x + 1) partial derivative/partial derivative y, we prove that the cyclicity of certain limit periodic sets is bounded by 1. The proposed method is applicable in any multi-parameter bifurcation problem and forms an extension to the known technique of "significant degeneration", i.e. the rescaling of parameters by means of different weights.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium.Smits, B, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
Document URI: http://hdl.handle.net/1942/3242
ISI #: 000072023200006
Type: Journal Contribution
Validations: ecoom 1999
Appears in Collections:Research publications

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