Limit theorems for translation flows (published version)

TL;DR

This paper derives asymptotic expansions and limit theorems for ergodic integrals of translation flows on higher genus flat surfaces, advancing understanding of their long-term statistical behavior.

Contribution

It provides new asymptotic and limit results specifically for translation flows on higher genus flat surfaces, extending previous work in ergodic theory.

Findings

Asymptotic expansion for ergodic integrals (Theorem 1)

Limit theorem for translation flows (Theorem 2)

Enhanced understanding of flow behavior on complex surfaces

Abstract

The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).