A Rational Interval of Rotation Numbers for Periodic Points in Certain NonSeparating Plane Continua.
Abstract
Let F be an orientation preserving homeomorphism of the plane that has a fixed point that is contained in an invariant, nonseparating continuum Lambda . If p/q is a reduced rational in the interior of the convex hull of the rotation set of Lambda about the fixed point, then there exists a qperiodic point in Lambda with rotation number p/q, provided that p/q is not the local rotation number about the fixed point and that Lambda satisfies certain technical requirements. We also show that the local rotation number is a point in the closure of the rotation set of Lambda and that if this rotation set is nondegenerate, then Lambda is indecomposable.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........37M
 Keywords:

 Mathematics, Physics: Astronomy and Astrophysics