TY - JOUR

T1 - Pseudo-anosov homeomorphisms on a sphere with four punctures have all periods

AU - Llibre, Jaume

AU - Mackay, Robert S.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - 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.

AB - 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.

U2 - https://doi.org/10.1017/S030500410007122X

DO - https://doi.org/10.1017/S030500410007122X

M3 - Article

SN - 0305-0041

VL - 112

SP - 539

EP - 549

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -