A Rational Interval of Rotation Numbers for Periodic Points in Certain Non-Separating Plane Continua.
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 q-periodic 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.
- Pub Date:
- January 1995
- Mathematics, Physics: Astronomy and Astrophysics