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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 368, Pages 122–129
(Mi znsl3507)
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This article is cited in 1 scientific paper (total in 1 paper)
Homoclinic processes and invariant measures for hyperbolic toral automorphisms
M. I. Gordin St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
For every hyperbolic toral automorphism $T$, the present author has defined in one of his previous papers some unbounded $T$-invariant second order difference operators related to the so-called homoclinic group of $T$. These operators were considered in the space $L_2$ with respect to the Haar measure. It is shown in the present paper that such operators give rise to transition semigroups in the space of continuous functions on the torus and generate dynamically invariant Markov processes. This leads almost immediately to a family of invariant measures for the automorphism $T$. After a short discussion, some open questions about properties of these measures and related topics are posed. Bibl. – 9 titles.
Key words and phrases:
hyperbolic toral automorphism, homoclinic group, invariant homoclinic operator, invariant Markov process, invariant probability measure.
Received: 02.12.2009
Citation:
M. I. Gordin, “Homoclinic processes and invariant measures for hyperbolic toral automorphisms”, Probability and statistics. Part 15, Zap. Nauchn. Sem. POMI, 368, POMI, St. Petersburg, 2009, 122–129; J. Math. Sci. (N. Y.), 167:4 (2010), 501–505
Linking options:
https://www.mathnet.ru/eng/znsl3507 https://www.mathnet.ru/eng/znsl/v368/p122
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Abstract page: | 169 | Full-text PDF : | 51 | References: | 33 |
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