An effective estimate for the Lebesgue measure of preimages of iterates of the Farey map

2015/03/25 by Byron Heersink, Heersink, Byron
Mathematics · #11J70 #11J83 #28A80 #37A45 (Primary) #40E05 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11J70 #msc:11J83 #msc:28A80 #msc:37A45 #msc:40E05

paper · pdf · doi:10.48550/arxiv.1503.07249

11 pages, 2 figures, added remark mentioning further results, made other minor revisions

arxiv created 2016/01/11 · arxiv updated 2016/01/12

Abstract

Using techniques from infinite ergodic theory, Kessebohmer and Stratmann determined the asymptotic behavior of the Lebesgue measure of sets of the form F^-n[α,β], where [α,β]⊆(0,1] and F is the Farey map. In this paper, we provide an effective version of this result, employing mostly basic properties of the transfer operator of the Farey map and an application of Freud's effective version of Karamata's Tauberian theorem.

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