Spectral analysis of time changes of horocycle flows
Rafael Tiedra De Aldecoa
Journal of Modern Dynamics 2012, 6(2): 275-285 doi: 10.3934/jmd.2012.6.275
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 commutator methods. time change spectral analysis

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