Sinai, YG

Ulcigrai, C

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.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

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

Abstract

Similar works

Full text

Available Versions

Explore Bristol Research