Journal of Modern Dynamics (JMD)

Spectral analysis of time changes of horocycle flows

Pages: 275 - 285, Issue 2, April 2012      doi:10.3934/jmd.2012.6.275

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Rafael Tiedra De Aldecoa - Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile (email)

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.

Keywords:  Horocycle flow, time change, spectral analysis, commutator methods.
Mathematics Subject Classification:  37C10, 37D40, 81Q10, 58J51.

Received: February 2012;      Available Online: August 2012.