On the struture of homeomorphims of the open annulus
Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a translation and we study the action of $h$ on the compactly connected components of the closed and without interior set ${\bf R}^2 \setminus O$.
Rotation numbers in the infinite annulus
Using the notion of free transverse triangulation we prove that the rotation number of a given probability measure invariant by a homeomorphism of the open annulus depends continuously on the homeomorphism under some boundedness conditions.
A simple proof of the Craig–Sakamoto theorem
Abstract We give a simple proof of the Craig–Sakamoto theorem, which asserts that two real symmetric matrices A and B satisfy det (I−aA−bB)= det (I−aA) det (I−bB) for all real numbers a and b if and only if AB=0 .