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Contraction groups and scales of automorphisms of totally disconnected locally compact groups
We study contraction groups for automorphisms of totally disconnected locally
compcat groups using the scale of the automorphism as a tool. The contraction
group is shown to be unbounded when the inverse automorphism has non-trivial
scale and this scale is shown to be the inverse value of the modular function
on the closure of the contraction group at the automorphism. The closure of the
contraction group is represented as acting on a homogenous tree and closed
contraction groups are characterised.Comment: revised version, 29 pages, to appear in Israel Journal of
Mathematics, please note that document starts on page
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