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.
Erratum : Stabilité simultanée de deux fonctions différentiables
Extension of Whitney Fields from Subanalytic Sets.
Families of functions dominated by distributions of -classes of mappings
A subsheaf of the sheaf of germs functions over an open subset of is called a sheaf of sub function. Comparing with the investigations of sheaves of ideals of , we study the finite presentability of certain sheaves of sub -rings. Especially we treat the sheaf defined by the distribution of Mather’s -classes of a mapping.
Families of spheres
Felix Klein's paper on real flexes vindicated
In a paper written in 1876 [4], Felix Klein gave a formula relating the number of real flexes of a generic real plane projective curve to the number of real bitangents at non-real points and the degree, which shows in particular that the number of real flexes cannot exceed one third of the total number of flexes. We show that Klein's arguments can be made rigorous using a little of the theory of singularities of maps, justifying in particular his resort to explicit examples.
Final forms for a three-dimensional vector field under blowing-up
We study the final situations which may be obtained for a singular vector field by permissible blowing-ups of the ambient space (in dimension three). These situations are preserved by permissible blowing-ups and its structure is simple from the view-point of the integral branches. Technically, we take a logarithmic approach, by marking in each step the exceptional divisor of the transformation.
Finite Determinacy and Topological Triviality I.
Finite determinacy and topological triviality. II : sufficient conditions and topological stability
Finitely Determined Singularities of Formal Vector Fields.
Fixed point indices of iterated maps.
Fonctions composées différentiables : cas algébrique
Soit un morphisme propre et de Nash d’un ouvert de dans un ouvert de . Nous démontrons que l’image par de l’algèbre des fonctions réelles dans est fermée dans munie de sa topologie habituelle d’espace de Fréchet. Ce résultat généralise, dans le cas algébrique, un résultat de G. Glaeser sur les fonctions composées différentiables.
Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
Formes tangentes à des actions commutatives
Fortsetzungen von C...-Funktionen, welche auf einer abgeschlossenen Menge in ...n definiert sind.
Framed holonomic knots.