R. de la Llave, R. Obaya
Decomposition theorems for groups of diffeomorphisms 
in the sphere
(57K, Latex 2.09)

ABSTRACT.   We study the algebraic structure of several
 groups of differentiable diffeomorphism
 in  $\sphere^n$.
 We show that given any  sufficiently smooth diffeomorphism
 can be written as the composition of
 a finite number of
 diffeomorphisms
 which are symmetric under reflection,
 essentially one-dimensional and
 about as differentiable as the
 given one.