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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Centralisers of $C^{\infty }$ diffeomorphisms
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by Boyd Anderson PDF
Trans. Amer. Math. Soc. 222 (1976), 97-106 Request permission

Abstract:

It is shown that if F is a hyperbolic contraction of ${R^n}$, coordinates may be chosen so that not only is F a polynomial mapping, but so is any diffeomorphism which commutes with F. This implies an identity principle for diffeomorphisms ${G_1}$ and ${G_2}$ commuting with an arbitrary Morse-Smale diffeomorphism F of a compact manifold M: if ${G_1},{G_2} \in Z(F)$, then ${G_1} = {G_2}$ on an open subset of $M \Rightarrow {G_1} \equiv {G_2}$ on M. Finally it is shown that under a certain linearisability condition at the saddles of F, $Z(F)$ is in fact a Lie group in its induced topology.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 97-106
  • MSC: Primary 58F99; Secondary 57D50
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0423424-6
  • MathSciNet review: 0423424