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Mosc. Math. J., 2009, Volume 9, Number 2, Pages 245–261 (Mi mmj344)  

This article is cited in 5 scientific papers (total in 5 papers)

Logarithmic asymptotics for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles

Alexander I. Bufetov

Department of Mathematics, Rice University, Houston, Texas

Abstract: A logarithmic asymptotics is obtained for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles, such that the norm of the corresponding renormalization matrix does not exceed a given value. The exponential growth rate of the number of such orbits is equal to the entropy of the flow.

Key words and phrases: periodic orbits, Teichmüller flow, suspension flows, moduli spaces, countable shifts.

DOI: https://doi.org/10.17323/1609-4514-2009-9-2-245-261

Full text: http://www.ams.org/.../abst9-2-2009.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37D25, 37A50, 37B40, 37C40
Received: March 3, 2008
Language:

Citation: Alexander I. Bufetov, “Logarithmic asymptotics for the number of periodic orbits of the Teichmüller flow on Veech's space of zippered rectangles”, Mosc. Math. J., 9:2 (2009), 245–261

Citation in format AMSBIB
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\by Alexander~I.~Bufetov
\paper Logarithmic asymptotics for the number of periodic orbits of the Teichm\"uller flow on Veech's space of zippered rectangles
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 2
\pages 245--261
\mathnet{http://mi.mathnet.ru/mmj344}
\crossref{https://doi.org/10.17323/1609-4514-2009-9-2-245-261}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2568438}
\zmath{https://zbmath.org/?q=an:1188.37001}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000271541500003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hamenstädt U., “Dynamics of the Teichmüller flow on compact invariant sets”, J. Mod. Dyn., 4:2 (2010), 393–418  crossref  mathscinet  zmath  isi  scopus
    2. Los Jérôme, “Infinite sequence of fixed-point free pseudo-Anosov homeomorphisms”, Ergodic Theory Dynam. Systems, 30:6 (2010), 1739–1755  crossref  mathscinet  zmath  isi  scopus
    3. Eskin A., Mirzakhani M., “Counting closed geodesics in moduli space”, J. Mod. Dyn., 5:1 (2011), 71–105  crossref  mathscinet  zmath  isi  scopus
    4. Eskin A., Mirzakhani M., Rafi K., “Counting Closed Geodesics in Strata”, Invent. Math., 215:2 (2019), 535–607  crossref  mathscinet  zmath  isi  scopus
    5. Forni G., Masur H., Smillie J., “Bill Veech'S Contributions to Dynamical Systems”, J. Mod. Dyn., 14 (2019), V–XXV  crossref  mathscinet  zmath  isi
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