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Singularities of vector fields on ℝ3 determined by their first non-vanishing jet

Published online by Cambridge University Press:  19 September 2008

Patrick Bonckaert ,
Freddy Dumortier  and
Sebastian Van Strien
Patrick Bonckaert
Affiliation:
Limburgs Universitair Centrum, B-3610 Diepenbeek, Belgium
Freddy Dumortier
Affiliation:
Limburgs Universitair Centrum, B-3610 Diepenbeek, Belgium
Sebastian Van Strien
Affiliation:
Math. Dept., T.U. Delft, PO Box 356, 2600 AJ Delft, The Netherlands
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Abstract

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In this paper we will present a result which gives a sufficient condition for a vector field X on ℝ3 to be equivalent at a singularity to the first non-vanishing jet jkX(p) of X at p. This condition - which only depends on the homogeneous vector field defined by jkX(p) - is stated in terms of the blown-up vector field (which is defined on S2xℝ), and essentially means that there are no saddleconnections for |S2×{0}.

The key tool in the proof will be a result of local normal linearization along a codimension 1 submanifold M providing a C0 conjugacy having a normal derivative along M equal to 1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 2 , June 1989 , pp. 281 - 308
Copyright
Copyright © Cambridge University Press 1989

References

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