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The rate of mixing for geodesic and horocycle flows. (English) Zbl 0623.22008
Author’s summary: “Using elementary methods we show that for every unitary representation \(\pi\) of \(G=SL(2, {\mathbb{R}})\) with no non-zero invariant vectors the matrix coefficients \(<\pi (a(t))v,w>\) of \[ a(t)=\left( \begin{matrix} e^ t\\ 0\end{matrix} \quad \begin{matrix} 0\\ e^{- t}\end{matrix} \right) \] decay exponentially fast for any vectors v, w Hölder continuous in the direction of the rotation subgroup of G.”
Reviewer: T.Jørgensen

MSC:
22D40 Ergodic theory on groups
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
22D10 Unitary representations of locally compact groups
22E40 Discrete subgroups of Lie groups
22E46 Semisimple Lie groups and their representations
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