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Nikolskii spaces were defined by way of translations on $R^{n}$ and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in $R^{n}$ , we get an equivalent definition if we replace translations by all isometries of $R^{n}$ . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...

Intertwined mappings

Jean Ecalle, Bruno Vallet (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Le type d'homotopie du groupe des difféomorphismes d'une surface compacte

André Gramain (1973)

Annales scientifiques de l'École Normale Supérieure

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

Given any compact manifold $M$ , we construct a non-empty open subset $𝒪$ of the space ${Diff}^{1} (M)$ of $C^{1}$ -diffeomorphisms and a dense subset $𝒟 \subset 𝒪$ such that the centralizer of every diffeomorphism in $𝒟$ is uncountable, hence non-trivial.

Maps Without Certain Singularities.

Andrew Du Plessis (1975)

Commentarii mathematici Helvetici

Normal forms for certain singularities of vectorfields

Floris Takens (1973)

Annales de l'institut Fourier

$C^{\infty}$ normal forms are given for singularities of $C^{\infty}$ vectorfields on $R$ , which are not flat, and for $C^{\infty}$ vectorfields $X$ on $R^{2}$ with $X (0) = 0$ , the 1-jet of $X$ in the origin is a pure rotation, and some higher order jet of $X$ attracting or expanding.