On Topological Stability of Divergent Diagrams of Folds.
Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
On local first order structural stability of pairings of vector fields and functions
Effective algebraic geometry and normal forms of reversible mappings.
We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.
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