Removable singularities for the Yang-Mills-Higgs equations in two dimensions
Restrictions of smooth functions to a closed subset
We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on extendability of functions. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek’s theorem on flatness.
Résultats nouveaux a propos des conjectures de Lichnerowicz et de Carathéodory
Rotation numbers for diffeomorphisms and flows
Simple singularities of functions on supermanifolds.
Singular Hamiltonian systems and symplectic capacities
The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless...
Singularités de bord : dualité, formules de Picard Lefschetz relatives et diagrammes de Dynkin
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Singularities of envelopes of families of submanifolds in
Singularities of k-tuples of vector fields [Book]
Singularities of the maximum function over a preimage
Singularities of Vector Fields on the Plane With Pointed Direction.
Smooth linearization of germs of -actions and holomorphic vector fields
The paper contains a generic condition permitting the linearization in class , , of germs of singular infinitesimal -actions on and of singular holomorphic...
Some combinatorial results about the operators with jumping nonlinearities
Some properties of the ring of germs of -functions
Some stability questions concerning caustics for different propagation laws.
Stabilité des applications différentiables
Stabilité simultanée de deux fonctions différentiables
Nous caractérisons les couples de fonctions différentiables , définies sur une variété compacte de dimension , qui sont simultanément stables en ce sens que, pour tout couple assez voisin, il existe un difféomorphisme de et deux difféomorphismes et de tels que et échangent et alors que et échangent et . L’outil essentiel est une technique de résolution des équations du type où les inconnues et sont des fonctions de classe .
Stability of Caustics.
Stability of Critical Points under Small Perturbations. Part II: Analytic Theory.