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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Hausdorff dimension and asymptotic cycles
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by Mark Pollicott PDF
Trans. Amer. Math. Soc. 355 (2003), 3241-3252 Request permission

Abstract:

We carry out a multifractal analysis for the asymptotic cycles for compact Riemann surfaces of genus $g \geq 2$. This describes the set of unit tangent vectors for which the associated orbit has a given asymptotic cycle in homology.
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Additional Information
  • Mark Pollicott
  • Affiliation: Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, England
  • MR Author ID: 140805
  • Received by editor(s): October 25, 2002
  • Published electronically: April 16, 2003
  • Additional Notes: I am very grateful to Howie Weiss and Luis Barreira for very useful conversations on multifractal analysis
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3241-3252
  • MSC (2000): Primary 28A78, 37D35; Secondary 37D40, 55N10
  • DOI: https://doi.org/10.1090/S0002-9947-03-03308-7
  • MathSciNet review: 1974685