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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bounds on least dilatations
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by R. C. Penner PDF
Proc. Amer. Math. Soc. 113 (1991), 443-450 Request permission


We consider the collection of all pseudo-Anosov homeomorphisms on a surface of fixed topological type. To each such homeomorphism is associated a real-valued invariant, called its dilatation (which is greater than one), and we define the spectrum of the surface to be the collection of logarithms of dilatations of pseudo-Anosov maps supported on the surface. The spectrum is a natural object of study from the topological, geometric, and dynamical points of view. We are concerned in this paper with the least element of the spectrum, and explicit upper and lower bounds on this least element are derived in terms of the topological type of the surface; train tracks are the main tool used in establishing our estimates.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 443-450
  • MSC: Primary 57N05; Secondary 32G15, 57M20, 58F18
  • DOI:
  • MathSciNet review: 1068128