Decomposition theorems for groups of diffeomorphisms in the sphere

Authors:
R. de la Llave and R. Obaya

Journal:
Trans. Amer. Math. Soc. **352** (2000), 1005-1020

MSC (1991):
Primary 58D05, 57S25, 57S05

Published electronically:
May 20, 1999

MathSciNet review:
1608297

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the algebraic structure of several groups of differentiable diffeomorphisms in . 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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Additional Information

**R. de la Llave**

Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

Email:
llave@math.utexas.edu

**R. Obaya**

Affiliation:
Departamento Matemática Aplicada a la Ingeniería, Escuela Superior de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid, Spain

Email:
rafoba@wmatem.eis.uva.es

DOI:
http://dx.doi.org/10.1090/S0002-9947-99-02320-X

Keywords:
Decomposition theorems,
diffeomorphism groups

Received by editor(s):
October 24, 1997

Published electronically:
May 20, 1999

Article copyright:
© Copyright 1999
American Mathematical Society