Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle |
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Authors: | Zaqueu Coelho Pierre Collet |
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Affiliation: | (1) Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 20570 (Ag. Iguatemi), 01498 São Paulo, SP, Brazil;(2) Ecole Polytechnique, Laboratoire UPR 14 du CNRS, Centre de Physique Théorique, F-91128 Palaiseau Cedex, France |
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Abstract: | Summary Given two pointsx, yS1 randomly chosen independently by a mixing absolutely continuous invariant measure of a piecewise expanding and smooth mapf of the circle, we consider for each >0 the point process obtained by recording the timesn>0 such that |fn(x)–fn(y)|. 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 explicity by an average on the rate of expansion off.Partially supported by FAPESP grant number 90/3918-5 |
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Keywords: | 60F05 60G55 34C35 |
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