showing 3 related works from this author
On singularities of discontinuous vector fields
2003
Abstract The subject of this paper concerns the classification of typical singularities of a class of discontinuous vector fields in 4D. The focus is on certain discontinuous systems having some symmetric properties.
Invariant varieties of discontinuous vector fields
2004
We study the geometric qualitative behaviour of a class of discontinuous vector fields in four dimensions around typical singularities. We are mainly interested in giving the conditions under which there exist one-parameter families of periodic orbits (a result that can be seen as one analogous to the Lyapunov centre theorem). The focus is on certain discontinuous systems having some symmetric properties. We also present an algorithm which detects and computes periodic orbits.
Reversible normal forms of degenerate cusps for planar diffeomorphisms
1998
Resume Dans cet article on donne des formes normales de germes a l'origine de diffeomorphismes reversibles du plan dont la partie lineaire est unipotente a valeurs propres positives. Le calcul de ces formes normales est base sur des algorithmes de geometrie algebrique effective. On etudie aussi des deformations generiques a k parametres (1 ≤ k ≤ 6).