Annular area preserving homeomorphisms which admit no interior compact invariant sets

TL;DR

This paper constructs a specific type of area-preserving homeomorphism on the annulus that is ergodic, isotopic to identity, has a prescribed irrational rotation number, and lacks interior compact invariant sets.

Contribution

It demonstrates the existence of ergodic, area-preserving homeomorphisms with prescribed irrational rotation numbers that have no interior compact invariant sets.

Findings

Existence of such homeomorphisms for any irrational rotation number

Homeomorphisms are ergodic and isotopic to identity

No interior compact invariant sets are present

Abstract

For any irrational number $\alpha$, there exists an ergodic area preserving homeomorphism of the closed annulus which is isotopic to the identitity, admits no compact invariant set contained in the interior of the annulus, and has the rotation number $\alpha$.