Mathematics – Dynamical Systems
Scientific paper
2009-08-21
Mathematics
Dynamical Systems
11 pages
Scientific paper
Let $\Gamma_A$ denote the abelian-by-cyclic group associated to an
integer-valued, non-singular matrix $A$. We show that if $A$ has no eigenvalues
of modulus one, then there are no faithful $C^1$ perturbations of the trivial
action $ \iota: \Gamma_A \to \diff$, where $M$ is a compact manifold.
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