Spectral analysis of time changes of horocycle flows

Rafael Tiedra De Aldecoa

doi:10.3934/jmd.2012.6.275

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2012, Volume 6, Issue 2: 275-285. Doi: 10.3934/jmd.2012.6.275

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Spectral analysis of time changes of horocycle flows

Rafael Tiedra De Aldecoa^1,

1.
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago

Received: January 31, 2012

Published: July 2012

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Abstract

We prove (under the condition of A. G. Kushnirenko) that all time changes of the horocycle flow have purely absolutely continuous spectrum in the orthocomplement of the constant functions. This provides an answer to a question of A. Katok and J.-P. Thouvenot on the spectral nature of time changes of horocycle flows. Our proofs rely on positive commutator methods for self-adjoint operators.

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Mathematics Subject Classification: 37C10, 37D40, 81Q10, 58J51.

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