Decomposition theorems for groups of diffeomorphisms in the sphere

de la Llave, R.; Obaya, R.

doi:10.1090/S0002-9947-99-02320-X

Decomposition theorems for groups of diffeomorphisms in the sphere
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by R. de la Llave and R. Obaya PDF

Trans. Amer. Math. Soc. 352 (2000), 1005-1020 Request permission

Abstract:

We study the algebraic structure of several groups of differentiable diffeomorphisms in $\mathbf {S}^n$. We show that any given 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.

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