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The structure of periodic point free distal homeomorphisms on the annulus
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abstract
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 $\mathbb R^2$.
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Linearizations of periodic point free distal homeomorphisms on the annulus
A distal annulus homeomorphism with invariant circle foliation is conjugate to a rotation whenever the foliation admits a continuous transversal, and non-linearizable examples exist for every irrational rotation number.
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