Skew products over rotations with exotic properties

TL;DR

This paper constructs specific skew product systems over rotations that exhibit unusual properties, including non-unique ergodicity, and explores their characteristics and related systems.

Contribution

It introduces new skew product constructions over rotations with exotic ergodic properties not previously documented.

Findings

Constructed a non-uniquely ergodic Z_2 skew product over a bounded quotient rotation.

Described properties of the constructed skew products.

Explored related Z skew products and their behaviors.

Abstract

We construct some skew products over rotations with strange properties. We construct a non-uniquely ergodic Z_2 skew product over a bounded quotient rotation. We describe some of its properties and related Z skew products.