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The loss of tightness of time distributions for homeomorphisms of the circle

Coelho, Z. (2004) The loss of tightness of time distributions for homeomorphisms of the circle. Transactions of the American Mathematical Society, 356 (11). pp. 4427-4445. ISSN 1088-6850

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For a minimal circle homeomorphism f we study convergence in law of rescaled hitting time point process of an interval of length epsilon > 0. Although the point process in the natural time scale never converges in law, we study all possible limits under a subsequence. The new feature is the fact that, for rotation numbers of unbounded type, there is a sequence epsilon(n) going to zero exhibiting coexistence of two non-trivial asymptotic limit point processes depending on the choice of time scales used when rescaling the point process. The phenomenon of loss of tightness of the first hitting time distribution is an indication of this coexistence behaviour. Moreover, tightness occurs if and only if the rotation number is of bounded type. Therefore tightness of time distributions is an intrinsic property of badly approximable irrational rotation numbers.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 11 Feb 2009 12:37
Last Modified: 11 Feb 2009 12:37
Published Version: http://dx.doi.org/10.1090/S0002-9947-04-03386-0
Status: Published
Publisher: American Mathematical Society
Identification Number: 10.1090/S0002-9947-04-03386-0
URI: http://eprints.whiterose.ac.uk/id/eprint/7761

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