Simple framed curve singularities
We obtain a complete list of simple framed curve singularities in ℂ² and ℂ³ up to the framed equivalence. We also find all the adjacencies between simple framed curves.
Simple singularities of functions on supermanifolds.
Singular fibers of stable maps and signatures of 4-manifolds.
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...
Singular holomorphic functions for which all fibre-integrals are smooth
For a germ (X,0) of normal complex space of dimension n + 1 with an isolated singularity at 0 and a germ f: (X,0) → (ℂ,0) of holomorphic function with df(x) ≤ 0 for x ≤ 0, the fibre-integrals , are on ℂ* and have an asymptotic expansion at 0. Even when f is singular, it may happen that all these fibre-integrals are . We study such maps and build a family of examples where also fibre-integrals for , the Grothendieck sheaf, are .
Singular open book structures from real mappings
We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
Singularités de bord : dualité, formules de Picard Lefschetz relatives et diagrammes de Dynkin
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Singularities and duality in the flat geometry of submanifolds of Euclidean spaces.
Singularities, defects and chaos in organized fluids
The singularities occurring in any sort of ordering are known in physics as defects. In an organized fluid defects may occur both at microscopic (molecular) and at macroscopic scales when hydrodynamic ordered structures are developed. Such a fluid system serves as a model for the study of the evolution towards a strong disorder (chaos) and it is found that the singularities play an important role in the nature of the chaos. Moreover both types of defects become coupled at the onset of turbulence....
Singularities of convex hulls as fronts of Legendre varieties
We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the front of a Legendre variety. Its singularities are classified up to contact diffeomorphism.
Singularities of envelopes of families of submanifolds in
Singularities of k-tuples of vector fields [Book]
Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space
In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.
Singularities of the Gauss map and the binormal surface.
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 properly critical subsets of Euclidean spaces.
Some quantitative results in singularity theory
The classical singularity theory deals with singularities of various mathematical objects: curves and surfaces, mappings, solutions of differential equations, etc. In particular, singularity theory treats the tasks of recognition, description and classification of singularities in each of these cases. In many applications of singularity theory it is important to sharpen its basic results, making them "quantitative", i.e. providing explicit and effectively computable estimates for all the important...