1991/12/01 by Marcy Barge, Richard M. Gillette · 1 citation
paper · doi:10.1017/s0143385700006398
Abstract We prove that if F is an orientation-preserving homeomorphism of the plane that leaves invariant a continuum Λ which irreducibly separates the plane into exactly two domains, then the convex hull of the rotation set of F restricted to Λ is a closed interval and each reduced rational in this interval is the rotation number of a periodic orbit in Λ. We also show that the interior and exterior rotation numbers of F associated with Λ are contained in the convex hull of the rotation set of F restricted to Λ and that if this set is nondegenerate then Λ is an indecomposable continuum.