Simple singularities of functions on supermanifolds.
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Singular Hamiltonian systems and symplectic capacities
Alfred Künzle (1996)
Banach Center Publications
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
Aviva Szpirglas (1990)
Bulletin de la Société Mathématique de France
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Nguyen Tien Dai, Nguyen Huu Duc, Frédéric Pham (1981)
Mémoires de la Société Mathématique de France
Singularities of envelopes of families of submanifolds in
Mário Jorge Dias Carneiro (1983)
Annales scientifiques de l'École Normale Supérieure
Singularities of k-tuples of vector fields [Book]
Bronisław Jakubczyk, Feliks Przytycki (1984)
Singularities of the maximum function over a preimage
Aleksey Davydov (1995)
Banach Center Publications
Singularities of Vector Fields on the Plane With Pointed Direction.
R.I. Bogdanov (1979)
Inventiones mathematicae
Smooth linearization of germs of -actions and holomorphic vector fields
F. Dumortier, Robert Roussarie (1980)
Annales de l'institut Fourier
The paper contains a generic condition permitting the linearization in class , , of germs of singular infinitesimal -actions on and of singular holomorphic...
Some stability questions concerning caustics for different propagation laws.
Romero Fuster, Maria del Carmen, Ruas, Maria Aparecida Soares (1994)
Portugaliae Mathematica
Stable mappings of 3-manifolds into the plane
Harold Levine (1988)
Banach Center Publications
Stokes' phenomenon; smoothing a victorian discontinuity
M. V. Berry (1988)
Publications Mathématiques de l'IHÉS
Stratifications of polynomial spaces
Lev Birbrair (1998)
Publicacions Matemàtiques
In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of R or C. We prove differential triviality of these stratifications. In the real case the proof is based on properties of the action of the group of interval exchange transformations on the set of all monic polynomials of some given degree. Finally we compare stratifications corresponding...
Sufficiency of Jets via Stratification Theory.
Tzee-Char Kuo, Yung-Chen Lu (1980)
Inventiones mathematicae
Sufficient decrease principle on Riemannian manifolds.
Udrişte, Constantin (1996)
Balkan Journal of Geometry and its Applications (BJGA)
Sur le théorème des fonctions composées différentiables
Jean-Jacques Risler (1982)
Annales de l'institut Fourier
Soit un morphisme propre relativement algébrique entre espaces semi-analytiques. On montre que si désigne l’anneau des fonctions de classe sur , l’image par de est fermée dans muni de sa topologie naturelle d’espace de Frechet ; ceci généralise un résultat précédent de J.-C. Tougeron (lui-même généralisant un résultat de Glaeser) qui traite du cas semi-algébrique. La méthode est tout à fait analogue et utilise des propriétés algébriques de l’anneau des fonctions Nash-analytiques introduit...
Sur les singularités des formes différentielles
Jean Martinet (1970)
Annales de l'institut Fourier
On étudie, sur le modèle de la théorie des singularités d’applications différentiables, les singularités des formes différentielles extérieures sur une variété différentiable. Les invariants fondamentaux utilisés sont le rang et la classe (au sens de E. Cartan) d’une forme différentielle. On étudie leur comportement générique à l’aide des théorèmes de transversalité. Par exemple, l’ensemble des points d’une variété de dimension où la classe d’une forme de Pfaff est égale à est génériquement...
Survey of recent results on singularities of equivariant maps
C. T. C. Wall (1988)
Banach Center Publications
Symmetric caustics and Curie's principle
Alain Joets, Ahmed Belaidi, Roland Ribotta (2003)
Banach Center Publications
Physical systems producing caustics may possess symmetries. In that case the relation between the symmetry of the system, considered as a whole, and the symmetry of the caustic follow a very general symmetry principle, the Curie principle. We give various examples of application of the Curie principle to caustics produced by the deflection of light in liquid crystals: the so called squint effect, the visualization of a new type of roll structure, etc. We show also that the Curie principle applies...
Symmetry Properties of Singularities of C°°-Functions.
Klaus Jänich (1978)
Mathematische Annalen
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