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Transactions of the American Mathematical Society

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



Hausdorff dimension and asymptotic cycles

Author: Mark Pollicott
Journal: Trans. Amer. Math. Soc. 355 (2003), 3241-3252
MSC (2000): Primary 28A78, 37D35; Secondary 37D40, 55N10
Published electronically: April 16, 2003
MathSciNet review: 1974685
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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

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
Article copyright: © Copyright 2003 American Mathematical Society