eldsASYMPTOTIC LIMIT LAW FOR THE CLOSEAPPROACH OF TWO TRAJECTORIES
نویسنده
چکیده
Given two points x; y 2 S 1 randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth map f of the circle, we consider for each " > 0 the point process obtained by recording the times n > 0 such that jf n (x) ? f n (y)j ". With the further assumption that the density of is bounded away from zero, we show that when " tends to zero the above point process scaled by " ?1 converges in law to a marked Poisson point process with constant parameter measure. This parameter measure is given explicitly by an average on the rate of expansion of f.
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