Three Brouwer fixed point theorems for homeomorphisms of the plane
We prove three theorems giving fixed points for orientation preserving homeomorphisms of the plane following forgotten results of Brouwer.
math.DS↗
arXiv subjects
Lucien Guillou
Publications and source records attributed to Lucien Guillou.
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 ${\bf R}^2 \setminus O$.
math.DS↗
Free lines for homeomorphisms of the open annulus
Let H be a homeomorphism of the open annulus isotopic to the identity which admits a lift h to the plane without fixed point. We show that h admits a Brouwer line which is a lift of a properly imbedded line joining one end to the other in the annulus or H admits a free essential simple closed curve.
math.DS↗