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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3395

Title: Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields
Authors: DUMORTIER, Freddy
IBANEZ MESA, Santiago
Issue Date: 1996
Publisher: ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS
Citation: JOURNAL OF DIFFERENTIAL EQUATIONS, 127(2). p. 590-647
Abstract: This paper deals with singularities of vector fields in R(3) having a 1-jet linear conjugate to y(partial derivative/partial derivative x) + z(partial derivative/partial derivative y). They first occur in generic 3-parameter families. In codimension 3 all such singularities are mutually C-D equivalent. We give a proof of this, provide a good normal form for 3-parameter unfoldings, and show that all non-wandering behaviour in such an unfolding is of small amplitude. We also show that for codimension 4 there are exactly 5 types of singularities for C-D equivalence. The proof relies on normal form theory, blowing-up, and estimation of Abelian integrals. (C) 1996 Academic Press, Inc.
Notes: UNIV OVIEDO,DEPT MATEMAT,E-33007 OVIEDO,SPAIN.Dumortier, F, LIMBURGS UNIV CENTRUM,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.
URI: http://hdl.handle.net/1942/3395
DOI: 10.1006/jdeq.1996.0085
ISI #: A1996UN29900013
ISSN: 0022-0396
Type: Journal Contribution
Appears in Collections: Research publications

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