An embedding theorem for homeomorphisms of the closed disc

Abstract:

If $f$ is an orientation preserving self-homeomorphism of the closed disc $D$ with the property that if $x,y \in D - N$, where the set of fixed points $N$ is finite and contained in $D - \operatorname {int} D$, then there exists an arc $A \subset D - N$ joining $x$ and $y$ such that ${f^n}(A)$ tends to a fixed point as $n \to \pm \infty$, then it is shown that $f$ can be embedded in a continuous flow on $D$.