de la Llave R., Obaya R.
Decomposition theorems for some groups of diffeomorphisms and
regularity of the composition operator
(90K, LaTeX)
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.