Stable Ergodicity of the Time-one Map of a Geodesic Ow
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Ergodicity of the Horocycle Flow
We prove that ergodicity of the horocycle ow on a surface of constant negative curvature is equivalent to ergodicity of the associated boundary action. As a corollary we obtain ergodicity of the horocycle ow on several large classes of covering surfaces. There are two natural \geometric ows" on (the unitary tangent bundle of) an arbitrary surface of constant negative curvature: the geodesic and...
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The paper is devoted to a study of the basic ergodic properties (ergodicity and conservativity) of the horocycle ow on surfaces of constant negative curvature with respect to the Liouville invariant measure. We give several criteria for ergodicity and conservativity and connect them with the classiication of the associated Fuchsian groups. Special attention is given to covering surfaces. In par...
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The notions of ergodicity (absence of non-trivial invariant sets) and conservativity (absence of non-trivial wandering sets) are basic for the theory of measure preserving transformations. Ergodicity implies conservativity, but the converse is not true in general. Nonetheless, transformations from some classes always happen to be either ergodic (hence, conservative), or completely dissipative (...
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