A limit theorem for Birkhoff sums of non-intetrable functions over rotations

YG Sinai, C Ulcigrai

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Abstract

We consider Birkhoff sums of functions with a singularity of type 1/x over rotations and prove the following limit theorem. Let S_N = SN (α, x)be the Nth non-renormalized Birkhoff sum, where α ∈ [0, 1) is the rotation number, x ∈ [0, 1) is the initial point and (α, x) are uniformly distributed. We prove that S_N /N has a joint limiting distribution in (α, x) as N tends to infinity. As a corollary, we get the existence of a limiting distribution for certain trigonometric sums.
Translated title of the contributionA limit theorem for Birkhoff sums of non-intetrable functions over rotations
Original languageEnglish
Title of host publicationGeometric and Probabilistic Structures in Dynamics
EditorsKeith Burns, Dimitry Dolgopyat, Yakov Pesin
PublisherAmerican Mathematical Society
Pages317 - 340
Number of pages24
VolumeContemporary Mathematics 469
ISBN (Print)9780821842867
Publication statusPublished - 2008

Fingerprint Dive into the research topics of 'A limit theorem for Birkhoff sums of non-intetrable functions over rotations'. Together they form a unique fingerprint.

Cite this