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Commutator criteria for strong mixing

Published online by Cambridge University Press:  21 July 2015

R. TIEDRA DE ALDECOA
R. TIEDRA DE ALDECOA*
Affiliation:
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile email rtiedra@mat.puc.cl
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Abstract

We present new criteria, based on commutator methods, for the strong mixing property of discrete flows $\{U^{N}\}_{N\in \mathbb{Z}}$ and continuous flows $\{e^{-itH}\}_{t\in \mathbb{R}}$ induced by unitary operators $U$ and self-adjoint operators $H$ in a Hilbert space ${\mathcal{H}}$ . Our approach put into light a general definition for the topological degree of the maps $N\mapsto U^{N}$ and $t\mapsto e^{-itH}$ with values in the unitary group of ${\mathcal{H}}$ . Among other examples, our results apply to skew products of compact Lie groups, time changes of horocycle flows and adjacency operators on graphs.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 1 , February 2017 , pp. 308 - 323
Copyright
© Cambridge University Press, 2015 

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