  Let $A$ be an annulus in the plane $\mathbb R^2$ and $g:A\rightarrow A$ 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 $\mathbb R^2$.
