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Special normal form of a hyperbolic CR-manifold in ℂ⁴

Vladimir V. Ežov, Gerd Schmalz (1998)

Annales Polonici Mathematici

We give a special normal form for a non-semiquadratic hyperbolic CR-manifold M of codimension 2 in ℂ⁴, i.e., a construction of coordinates where the equation of M satisfies certain conditions. The coordinates are determined up to a linear coordinate change.

Stabilité des systèmes à commutations du plan

Ugo Boscain, Grégoire Charlot, Mario Sigalotti (2009/2010)

Séminaire de théorie spectrale et géométrie

Soient X et Y deux champs de vecteurs lisses sur 2 globalement asymptotiquement stables à l’origine. Nous donnons des conditions nécessaires et des conditions suffisantes sur la topologie de l’ensemble des points où X et Y sont parallèles pour pouvoir assurer la stabilité asymptotique globale du système contrôlé non linéaire non autonome q ˙ ( t ) = u ( t ) X ( q ( t ) ) + ( 1 - u ( t ) ) Y ( q ( t ) ) où le contrôle u est une fonction mesurable arbitraire de [ 0 , + [ dans { 0 , 1 } . Les conditions données ne nécessitent aucune intégration ou construction d’une fonction de Lyapunov...

Stein open subsets with analytic complements in compact complex spaces

Jing Zhang (2015)

Annales Polonici Mathematici

Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, H i ( Y , Y ) = 0 for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that Φ | n D | - 1 ( Φ | n D | ( x ) ) Y is empty or has dimension 0, where Φ | n D | is the map from...

Stratified Whitney jets and tempered ultradistributions on the subanalytic site

N. Honda, G. Morando (2011)

Bulletin de la Société Mathématique de France

In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X . Then, we define stratified ultradistributions of Beurling and Roumieu type on X . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X . Second, the tempered-stratified...

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