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Transactions of the American Mathematical Society

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



Centralisers of $C^{\infty }$ diffeomorphisms

Author: Boyd Anderson
Journal: Trans. Amer. Math. Soc. 222 (1976), 97-106
MSC: Primary 58F99; Secondary 57D50
MathSciNet review: 0423424
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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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Article copyright: © Copyright 1976 American Mathematical Society