The structure of periodic point free distal homeomorphisms on the annulus

Abstract

Let $A$ be an annulus in the plane ${\mathbb{R}}^2$ and $g:A\to A$ be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is a continuous decomposition of $A$ into $g$-invariant circles such that all the restrictions of $g$ on them share a common irrational rotation number and all these circles are linearly ordered by the inclusion relation on the sets of bounded components of their complements in ${\mathbb{R}}^2$.

18 pages. Comments are welcome