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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 408, Pages 131–153
(Mi znsl5497)
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This article is cited in 2 scientific papers (total in 2 papers)
Poisson limit for two-dimensional toral automorphisms driven by continued fractions
M. Gordinab, M. Denkerc a St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
c Department of Mathematics, McAllister Building, Pennsylvania State University, University Park, PA 16802, USA
Abstract:
Generalizing powers of a single hyperbolic automorphism of the two-dimensional torus, we consider some class of sequences of such automorphisms. Technically such sequences are determined by means of continued fraction expansions of a pair of real numbers. As a substitute for the pair of foliations in the classical hyperbolic theory, every sequence of this class has a sequence of asymptotically stable and a sequence of asymptotically unstable foliations. We prove a kind of the Poisson limit theorem for such sequences extending a method used earlier by A. Sharova and the present authors to prove a Poisson limit theorem for powers of a single hyperbolic automorphisms of the torus. Possible generalizations are briefly discussed.
Key words and phrases:
toral automorphisms, Poisson limit, Chen–Stein method, homoclinic structures, boundary behavior.
Received: 05.10.2012
Citation:
M. Gordin, M. Denker, “Poisson limit for two-dimensional toral automorphisms driven by continued fractions”, Probability and statistics. Part 18, Zap. Nauchn. Sem. POMI, 408, POMI, St. Petersburg, 2012, 131–153; J. Math. Sci. (N. Y.), 199:2 (2014), 139–149
Linking options:
https://www.mathnet.ru/eng/znsl5497 https://www.mathnet.ru/eng/znsl/v408/p131
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Abstract page: | 157 | Full-text PDF : | 58 | References: | 30 |
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