92-7 de la Llave R., Obaya R.

Decomposition theorems for some groups of diffeomorphisms and regularity of the composition operator (90K, LaTeX) Feb 2, 92

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Abstract. We study the algebraic structure of several diffeomorphism groups in $\sphere^n$. We show that all diffeomorphisms can be written as a finite product of diffeomorphisms which have certain symmetries. Since the natural group operation among diffeomorphisms is the composition and H\"older regularities appear naturally in intermediate steps, we present an appendix in which optimal results about regularity of the composition operator are obtained when the spaces of diffeomorphisms are given the topology of the classical H\"older norms.

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