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In this paper we show to what extent the closed, singular 2-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed 2-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures....

Geometry of some simple nonlinear differential operators

H. P. Mc Kean, J. C. Scovel (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie

F. Dumortier, Robert Roussarie (1983)

Annales de l'institut Fourier

Pour tout triplet d’entiers $s, k, ℓ$ tels que $0 \leq s \leq k \leq ℓ$ , se pose la question d’étudier les germes de difféomorphismes ou de champs de vecteurs sur $R^{n}$ , de classe $ℓ$ , $k$ -déterminés en classe $s$ , c’est-à-dire respectivement conjugués ou équivalents en classe $s$ , à tout germe ayant la même classe $ℓ$ et le même $k$ -jet. Cette question est abordée ici, avec quelque généralité en dimension 2 et pour les germes de champs de vecteurs de codimension 2, en dimension 3 et 4. Une conséquence de cette dernière étude est l’existence...

Global Families of Local Unfoldings.

Klaus Jänich (1979)

Mathematische Annalen

Global stability for diagrams of differentiable applications

Luis Antonio Favaro, C. M. Mendes (1986)

Annales de l'institut Fourier

In this paper, we give some examples which point to the non-existence of $C^{\infty}$ -global stable diagrams $R \overset{g}{\leftarrow} M \overset{f}{\to} R$ , $M$ compact. If $Φ$ : $M \to Q$ is fixed we define the $Φ$ -equivalence for maps $f : M \to P$ and the corresponding $Φ$ -stability. The globalization procedure works and we can compare the $Φ$ -stability, $Φ$ -infinitesimal stability, and $Φ$ -homotopical stability. Also we give some characterization theorems for lower dimensions.

Globally invertible differentiable or holomorphic maps

E. Ballico (2001)

Rendiconti del Seminario Matematico della Università di Padova

Hausdorff measures and the Morse-Sard theorem.

Carlos Gustavo T. de A. Moreira (2001)

Publicacions Matemàtiques

Let F : U ⊂ Rn → Rm be a differentiable function and p < m an integer. If k ≥ 1 is an integer, α ∈ [0, 1] and F ∈ Ck+(α), if we set Cp(F) = {x ∈ U | rank(Df(x)) ≤ p} then the Hausdorff measure of dimension (p + (n-p)/(k+α)) of F(Cp(F)) is zero.

Holomorphic extension maps for spaces of Whitney jets.

Jean Schmets, Manuel Valdivia (2001)

RACSAM

The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.

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Function germs defined on isolated hypersurface singularities

Functions of class $C^{k}$ .

Generic bifurcations of second order ordinary differential equations on differentiable manifolds

Generic Bifurcations of Varieties.

Generic Bifurcations of Varieties II.

Generic deformations of Lagrangian and Legendrian maps

Generic differentiability of mappings and convex functions in Banach and locally convex spaces

Geometric objects with finitely determined germs

Geometry and representation of the singular symplectic forms

Geometry of some simple nonlinear differential operators

Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie

Global Families of Local Unfoldings.

Global stability for diagrams of differentiable applications

Globally invertible differentiable or holomorphic maps

Hausdorff measures and the Morse-Sard theorem.

Holomorphic extension maps for spaces of Whitney jets.

Homotopien von Untermannigfaltigkeiten mit nicht ausgearteter zweiter Fundamentalform

Homotopy classification of regular sections

How to Get around a Simple Quadratic Fold.

Il teorema di Morse-Sard in spazi di Sobolev Problemi di trasporto ottimale e applicazioni

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