Catastrophe models and the expansion method: A review of issues and an application to the econometric modeling of economic growth.
Caustics and wave front propagations: applications to differential geometry
This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.
Caustique mystique
Caustiques et catastrophes
Characteristic vector fields of generic distributions of corank 2
Characterizations of -sufficiency of jets
Classification C...des équations de pfaff complètement intégrables à singularité isolée.
Classification of relative minima singularities
Classification of -simple germs from to
Classification of singularities at infinity of polynomials of degree 4 in two variables.
Classification of singularities with compact abelian symmetry
Classifying Spaces of b-Stable Whitney Coverings.
Close cohomologous Morse forms with compact leaves
We study the topology of foliations of close cohomologous Morse forms (smooth closed 1-forms with non-degenerate singularities) on a smooth closed oriented manifold. We show that if a closed form has a compact leave , then any close cohomologous form has a compact leave close to . Then we prove that the set of Morse forms with compactifiable foliations (foliations with no locally dense leaves) is open in a cohomology class, and the number of homologically independent compact leaves does not decrease...
Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs.
Codimension 4 singularities on reflectionally symmetryc planar vector fields.
The paper deals with the topological classification of singularities of vector fields on the plane which are invariant under reflection with respect to a line. As it has been proved in previous papers, such a classification is necessary to determine the different topological types of singularities of vector fiels on R3 whose linear part is invariant under rotations. To get the classification we use normal form theory and the the blowing-up method.
Coisotropic varieties and their generating families
Combinatorial structure of Stokes regions of a simple singularity.
Computing the differential of an unfolded contact diffeomorphism
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
Conformally invariant variational integrals and the removability of isolated singularities.
Constructing generic smooth maps of a manifold into a surface with prescribed singular loci
It is known that the singular set of a generic smooth map of an -dimensional manifold into a surface is a closed 1-dimensional submanifold of and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.