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Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3

Published online by Cambridge University Press:  19 September 2008

F. Dumortier ,
R. Roussarie  and
J. Sotomayor
F. Dumortier
Affiliation:
Limburgs Universitair Centrum, Universitair Campus, B-3610 Diepenbeek, Belgium;
R. Roussarie
Affiliation:
Laboratoire de Topologie, U.A. 755 du CNRS, Université de Bourgogne, B.P. 138-21004-Dijon, France;
J. Sotomayor
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460 Jardim Botânico, Rio de Janeiro, Brazil
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Abstract

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A cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate to

We define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent to

Our main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 3 , September 1987 , pp. 375 - 413
Copyright
Copyright © Cambridge University Press 1987

References

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