Ergodicity for Infinite Periodic Translation Surfaces

TL;DR

This paper proves that for certain infinite translation surfaces with lattice structures and infinite strips, almost all straight-line flows are ergodic, advancing understanding of dynamical behavior on such surfaces.

Contribution

It establishes ergodicity for almost every direction on Z-covers of lattice translation surfaces with infinite strips, a novel result in the dynamics of infinite surfaces.

Findings

Almost every direction yields ergodic straight-line flow.

The result applies to Z-covers of lattice surfaces with infinite strips.

Provides new insights into the dynamics of infinite translation surfaces.

Abstract

For a Z-cover of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.