Éclatements quasi homogènes
Économie et théorie des catastrophes
Les hypothèses de différentiabilité jouent un rôle essentiel dans plusieurs travaux récents consacrés à l'étude des propriétés de l'équilibre économique. Cet article présente une synthèse aussi élémentaire que possible d'une partie de ces travaux et fait aussi le lien avec la théorie des catastrophes de Thom.
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.
Eine Bemerkung zur Regularität stationärer Punkte von konform invarianten Variationsintegralen.
Elliptic K3 surfaces as dynamical models and their Hamiltonian monodromy
This note deals with Lagrangian fibrations of elliptic K3 surfaces and the associated Hamiltonian monodromy. The fibration is constructed through the Weierstraß normal form of elliptic surfaces. There is given an example of K3 dynamical models with the identity monodromy matrix around 12 elementary singular loci.
Equivalence and zero sets of certain maps in infinite dimensions
Equivalence and zero sets of certain maps on infinite dimensional spaces are studied using an approach similar to the deformation lemma from the singularity theory.
Equivalence of differentiable functions, rational functions and polynomials
We show under some assumptions that a differentiable function can be transformed globally to a polynomial or a rational function by some diffeomorphism. One of the assumptions is that the function is proper, the number of critical points is finite, and the Milnor number of the germ at each critical point is finite.
Equivalence of differentiable mappings and analytic mappings
Equivalence of generic mappings and normalization
Equivalence of Glancing Hypersurfaces. II.
Extension of Whitney Fields from Subanalytic Sets.