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

Jaume Llibre, Robert S. Mackay

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16 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)539-549
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusPublished - 1 Jan 1992


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