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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.

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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