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PSEUDO-ANOSOV HOMEOMORPHISMS ON A SPHERE WITH 4 PUNCTURES HAVE ALL PERIODS
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UNSPECIFIED (1992) PSEUDO-ANOSOV HOMEOMORPHISMS ON A SPHERE WITH 4 PUNCTURES HAVE ALL PERIODS. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 112 (Part 3). pp. 539-549. ISSN 0305-0041.
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Abstract
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 greater-than-or-equal-to 7 we give examples of pseudo-Anosov homeomorphisms of the sphere, relative to a set of N points, for which not all periods occur.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0305-0041 | ||||
Official Date: | November 1992 | ||||
Dates: |
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Volume: | 112 | ||||
Number: | Part 3 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 539-549 | ||||
Publication Status: | Published |
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