On uniformly distributed orbits of certain horocycle flows

Dani, S. G. (1982) On uniformly distributed orbits of certain horocycle flows Ergodic Theory & Dynamical Systems, 2 (2). pp. 139-158. ISSN 0143-3857

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0143385700001474

Abstract

G = SL (2,R), Γ=SL(2,Z), u1 = (10l1)(where t ε R) and let μ be the G-invariant probability measure on G/Gamma. We show that if x is a non-periodic point of the flow given by the (ut)-action on G/Gamma then the (ut)-orbit of x is uniformly distributed with respect to μ ; that is, if Ω is an open subset whose boundary has zero measure, and l is the Lebesque measure on R then, as T→∞T-1{0≤t≤ T\utxεΩ} , converges to μ (Ω).

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