Unfoldings Knot Theory (Corrigendum).
Unfoldings of foliations with multiform first integrals
Let be a codim 1 local foliation generated by a germ of the form for some complex numbers and germs of holomorphic functions at the origin in . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for is equivalent to the unfolding theory for the multiform function...
Unfoldings of Meromorphic Functions.
Unique Normal Forms for Planar Vector Fields.
Universal Families of C°°-Functions on D2.
Universal topological stratification for the Pham example
Universelle Familien differenzierbarer Funktionen auf der Kreislinie.
[unknown]
Valeurs critiques asymptotiques d'une fonction définissable dans une structure o-minimale
We prove that the set of asymptotic critical values of a function definable in an o-minimal structure is finite, even if the structure is not polynomially bounded. As a consequence, the function is a locally trivial fibration over the complement of this set.
Vanishing cohomology of singularities of mappings
Variation du nombre de Lefschetz dans une famille d'automorphismes analytiques.
Volume and multiplicities of real analytic sets
We give criteria of finite determinacy for the volume and multiplicities. Given an analytic set described by {v = 0}, we prove that the log-analytic expansion of the volume of the intersection of the set and a "little ball" is determined by that of the set defined by the Taylor expansion of v up to a certain order if the mapping v has an isolated singularity at the origin. We also compare the cardinalities of finite fibers of projections restricted to such a set.
Waves of excitations in heterogeneous annular region, asymmetric arrangement
This paper deals with the propagation of waves around a circular obstacle. The medium is heterogeneous: the velocity is smaller in the inner region and greater in the outer region. The interface separating the two regions is also circular, and the obstacle is located eccentrically inside it. The different front portraits are classified.
Waves of excitations in heterogeneous annular region II. Strong asymmetry
Excitation wave propagation in a heterogeneous medium around a circular obstacle is investigated, when the obstacle is located very eccentrically with respect to the interfacial circle separating the slow inner and the fast outer region. Qualitative properties of the permanent wave fronts are described, and the calculated wave forms are presented.
-constant monodromy groups and marked singularities
-constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo . Second, marked singularities are defined and global moduli spaces for right equivalence...
Нормальная форма медленных движений уравнения релаксационного типа и расслоения биномиальных поверхностей
Особенности выпуклых оболочек
Особенности полей предельных направлений двумерных управляемых систем
Отображение периодов и дискриминант
Продолжение CR-функций в клин с многообразия конечного типа