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Title: Singularities of vector fields on IR-3
Authors: DUMORTIER, Freddy 
IBANEZ MESA, Santiago 
Issue Date: 1998
Source: NONLINEARITY, 11(4). p. 1037-1047
Abstract: In his well known paper 'Singularities of vector fields', Takens made a topological classification of vector fields up to codimension 2 and introduced a semialgebraic stratification to distinguish the different cases; from dimensions greater than or equal to 3 he had to use the notion of 'weak-C-0-equivalence'. In this paper we show how to classify singularities of vector fields on R-3 up to codimension 4 for the notion of C-0 equivalence. To separate the different cases we use a semianalytic stratification and show that a semialgebraic one is not possible, even for the notion of weak-C-0-equivalence. Up to codimension 3 the stratification is semialgebraic. We will always suppose that the vector fields are C-infinity, although it will be clear that the results are valid for C-r, with r sufficiently big. We provide a complete, but short, survey of the different techniques to be used, referring to the existing literature for precise calculations and pictures. We put much emphasis on the new results.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium. Univ Oviedo, Dept Matemat, Oviedo 33007, Spain.Dumortier, F, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
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ISI #: 000074936900015
Type: Journal Contribution
Validations: ecoom 1999
Appears in Collections:Research publications

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