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Transactions of the American Mathematical Society

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

 

 

Centralisers of $ C\sp{\infty }$ diffeomorphisms


Author: Boyd Anderson
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1976-0423424-6
Article copyright: © Copyright 1976 American Mathematical Society