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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Decomposition theorems for groups of diffeomorphisms in the sphere
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by R. de la Llave and R. Obaya
Trans. Amer. Math. Soc. 352 (2000), 1005-1020
DOI: https://doi.org/10.1090/S0002-9947-99-02320-X
Published electronically: May 20, 1999

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.
References
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Bibliographic 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
  • Received by editor(s): October 24, 1997
  • Published electronically: May 20, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 1005-1020
  • MSC (1991): Primary 58D05, 57S25, 57S05
  • DOI: https://doi.org/10.1090/S0002-9947-99-02320-X
  • MathSciNet review: 1608297