It is proved that if f is a homeomorphism of the two-sphere with an invariant set V of cardinality N = 4, then either f has periodic orbits of all periods or it belongs to one of a small number of algebraically finite isotopy classes relative to V. For N < 4, the second case always holds. On the other hand, for each N ≥ 7 we give examples of pseudo-Anosov homeomorphisms of the sphere, relative to a set of N points, for which not all periods occur. © 1992, Cambridge Philosophical Society. All rights reserved.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 1 Jan 1992|