Abstract
For the strong unstable foliation (or horocycle foliation) of an Anosov flow there exists a unique transverse measure called the Margulis measure. In this paper we extend Margulis' results to more general “transverse distributions” for the foliation. As an application we derive our main result: The non-zero analytic extension to a strip of the Selberg zeta function for compact surfaces of constant negative curvature persists under small perturbations in the metric. There is an equivalent formulation in terms of the Fourier transform of the correlation function.
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Communicated by J.-P. Eckmann
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Pollicott, M. Margulis distributions for Anosov flows. Commun.Math. Phys. 113, 137–154 (1987). https://doi.org/10.1007/BF01221402
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DOI: https://doi.org/10.1007/BF01221402