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Uspekhi Mat. Nauk, 1998, Volume 53, Issue 2(320), Pages 3–106 (Mi umn17)  

This article is cited in 39 scientific papers (total in 39 papers)

Thermodynamic formalism for countable symbolic Markov chains

B. M. Gurevicha, S. V. Savchenkob

a M. V. Lomonosov Moscow State University
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm17

Full text: PDF file (908 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1998, 53:2, 245–344

Bibliographic databases:

UDC: 519.217
MSC: 37D35, 60J27, 37B10, 37C30
Received: 18.12.1997

Citation: B. M. Gurevich, S. V. Savchenko, “Thermodynamic formalism for countable symbolic Markov chains”, Uspekhi Mat. Nauk, 53:2(320) (1998), 3–106; Russian Math. Surveys, 53:2 (1998), 245–344

Citation in format AMSBIB
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    2. S. V. Savchenko, “Spectral properties of an indecomposable non-negative matrix and its principal submatrices of co-order one”, Russian Math. Surveys, 55:1 (2000), 184–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. A. M. Vershik, “Dynamic theory of growth in groups: Entropy, boundaries, examples”, Russian Math. Surveys, 55:4 (2000), 667–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Sarig, OM, “On an example with a non-analytic topological pressure”, Comptes Rendus de l Academie Des Sciences Serie i-Mathematique, 330:4 (2000), 311  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Mauldin R.D., Urbański M., “Gibbs states on the symbolic space over an infinite alphabet”, Israel J. Math., 125:1 (2001), 93–130  crossref  mathscinet  zmath  isi  scopus  scopus
    6. A. B. Polyakov, “On a measure with maximal entropy for the special flow on a local perturbation of a countable topological Bernoulli scheme”, Sb. Math., 192:7 (2001), 1001–1024  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    8. Fiebig D., Fiebig U.-R., Yuri M., “Pressure and equilibrium states for countable state Markov shifts”, Israel J. Math., 131:1 (2002), 221–257  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Ruette S., “On the Vere–Jones classification and existence of maximal measures for countable topological Markov chai”, Pacific J Math, 209:2 (2003), 365–380  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Buzzi J., Sarig O., “Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps”, Ergodic Theory Dynam. Systems, 23:5 (2003), 1383–1400  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Gómez R., “Positive $K$-theory for finitary isomorphisms of Markov chains”, Ergodic Theory Dynam. Systems, 23:5 (2003), 1485–1504  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Buzzi J., “Subshifts of quasi-finite type”, Invent. Math., 159:2 (2005), 369–406  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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    18. Buzzi, J, “Maximal entropy measures for piecewise affine surface homeomorphisms”, Ergodic Theory and Dynamical Systems, 29 (2009), 1723  crossref  mathscinet  zmath  isi  scopus  scopus
    19. Cyr, V, “Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts”, Communications in Mathematical Physics, 292:3 (2009), 637  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    20. Gomez, R, “Spanning tree invariants, loop systems and doubly stochastic matrices”, Linear Algebra and Its Applications, 432:2–3 (2010), 556  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Buzzi J., “Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps”, Annales de l Institut Fourier, 60:3 (2010), 801–852  crossref  mathscinet  zmath  isi  scopus  scopus
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    23. Araujo V., Bufetov A.I., “A large deviations bound for the Teichmüller flow on the moduli space of abelian differentials”, Ergodic Theory Dynam Systems, 31:4 (2011), 1043–1071  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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    25. Bruin H., Todd M., “Transience and Thermodynamic Formalism for Infinitely Branched Interval Maps”, J. Lond. Math. Soc.-Second Ser., 86:Part 1 (2012), 171–194  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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    34. Ledrappier F., “Erratum: On Omri Sarig's work on the dynamics of surfaces”, J. Mod. Dyn., 9 (2015), 355  crossref  mathscinet  zmath  isi  scopus
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