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), u_{1} = (^{1}_{0}^{l}_{1})(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 (u_{t})-action on G/Gamma then the (u_{t})-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\u_{t}xεΩ} , converges to μ (Ω).

Item Type: | Article |
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Source: | Copyright of this article belongs to Cambridge University Press. |

ID Code: | 8221 |

Deposited On: | 26 Oct 2010 12:09 |

Last Modified: | 30 May 2011 06:15 |

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