RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1967, Volume 22, Issue 5(137), Pages 81–106 (Mi umn5791)  

This article is cited in 59 scientific papers (total in 59 papers)

Approximations in ergodic theory

A. B. Katok, A. M. Stepin


Full text: PDF file (2579 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1967, 22:5, 77–102

Bibliographic databases:

UDC: 519.9
MSC: 37A25, 37A35, 55R10, 37A30
Received: 14.11.1966

Citation: A. B. Katok, A. M. Stepin, “Approximations in ergodic theory”, Uspekhi Mat. Nauk, 22:5(137) (1967), 81–106; Russian Math. Surveys, 22:5 (1967), 77–102

Citation in format AMSBIB
\Bibitem{KatSte67}
\by A.~B.~Katok, A.~M.~Stepin
\paper Approximations in ergodic theory
\jour Uspekhi Mat. Nauk
\yr 1967
\vol 22
\issue 5(137)
\pages 81--106
\mathnet{http://mi.mathnet.ru/umn5791}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=219697}
\zmath{https://zbmath.org/?q=an:0172.07202}
\transl
\jour Russian Math. Surveys
\yr 1967
\vol 22
\issue 5
\pages 77--102
\crossref{https://doi.org/10.1070/RM1967v022n05ABEH001227}


Linking options:
  • http://mi.mathnet.ru/eng/umn5791
  • http://mi.mathnet.ru/eng/umn/v22/i5/p81

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Katok, A. M. Stepin, “Metric properties of measure preserving homeomorphisms”, Russian Math. Surveys, 25:2 (1970), 191–220  mathnet  crossref  mathscinet  zmath
    2. D. V. Anosov, A. B. Katok, “Novye primery ergodicheskikh diffeomorfizmov gladkikh mnogoobrazii”, UMN, 25:4(154) (1970), 173–174  mathnet  mathscinet  zmath
    3. A. M. Stepin, “Cohomologies of automorphism groups of a Lebesgue space”, Funct. Anal. Appl., 5:2 (1971), 167–168  mathnet  crossref  mathscinet  zmath
    4. V. I. Oseledets, “Two nonisomorphic dynamical systems with the same simple continuous spectrum”, Funct. Anal. Appl., 5:3 (1971), 233–236  mathnet  crossref  mathscinet  zmath
    5. D. V. Anosov, “Existence of smooth ergodic flows on smooth manifolds”, Math. USSR-Izv., 8:3 (1974), 525–552  mathnet  crossref  mathscinet  zmath
    6. E. A. Sataev, “On the number of invartiant measures for flows on orientable surfaces”, Math. USSR-Izv., 9:4 (1975), 813–830  mathnet  crossref  mathscinet  zmath
    7. M. Casartelli, L. Galgani, A. Scotti, “Numerical computations on a stochastic parameter related to the Kolmogorov entropy”, Phys Rev A, 13:5 (1976), 1921  crossref  adsnasa
    8. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
    9. A. B. Katok, “Monotone equivalence in ergodic theory”, Math. USSR-Izv., 11:1 (1977), 99–146  mathnet  crossref  mathscinet  zmath  isi
    10. G. W. Riley, “Approximations and the spectral properties of measure-preserving group actions”, Isr J Math, 33:1 (1979), 9  crossref  mathscinet  zmath
    11. V. A. Chulaevskii, “Cyclic approximations of interval exchange transformations”, Russian Math. Surveys, 34:2 (1979), 221–222  mathnet  crossref  mathscinet  zmath
    12. G. R. Goodson, P. N. Whitman, “A SKEW-PRODUCT WITH SIMPLE SINGULAR SPECTRUM”, Quaestiones Mathematicae, 4:4 (1981), 309  crossref
    13. G. R. Goodson, “SPECIAL AUTOMORPHISMS WITH CONTINUOUS SPECTRUM”, Quaestiones Mathematicae, 5:3 (1982), 243  crossref
    14. Richard J Turek, “Approximation and ergodic theorems”, Advances in Mathematics, 51:3 (1984), 258  crossref
    15. S Aubry, K Fesser, A R Bishop, J Phys A Math Gen, 18:16 (1985), 3157  crossref  mathscinet  adsnasa  isi
    16. S. Aubry, K. Fesser, A. R. Bishop, “Locking to incommensurate structures”, Ferroelectrics, 66:1 (1986), 151  crossref
    17. Mahesh G. Nerurkar, “On the construction of smooth ergodic skew-products”, Ergod Th Dynam Sys, 8:2 (1988)  crossref  mathscinet  zmath
    18. O. N. Ageev, “Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum”, Math. USSR-Sb., 64:2 (1989), 305–317  mathnet  crossref  mathscinet  zmath
    19. V. V. Ryzhikov, “Joinings, intertwining operators, factors, and mixing properties of dynamical systems”, Russian Acad. Sci. Izv. Math., 42:1 (1994), 91–114  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. O. N. Ageev, “Mixing in the components and rearrangements of $T_{\alpha,\beta}$”, Russian Math. Surveys, 49:2 (1994), 141–142  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. Ulrike Feudel, Arkady S. Pikovsky, Michael A. Zaks, “Correlation properties of a quasiperiodically forced two-level system”, Phys Rev E, 51:3 (1995), 1762  crossref  isi
    22. A. A. Prikhod'ko, “Special representation of an aperiodic automorphism of a Lebesgue space”, Math. Notes, 58:2 (1995), 891–893  mathnet  crossref  mathscinet  zmath  isi
    23. A. Hof, “On a “structure intermediate between quasiperiodic and random””, J Statist Phys, 84:1-2 (1996), 309  crossref  mathscinet  zmath  adsnasa  isi
    24. Ulrike Feudel, Arkady Pikovsky, Antonio Politi, J Phys A Math Gen, 29:17 (1996), 5297  crossref  mathscinet  zmath  isi
    25. V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. Z. I. Bezhaeva, V. I. Oseledets, “Concerning a stochastic dynamical system”, Math. Notes, 61:6 (1997), 675–680  mathnet  crossref  crossref  mathscinet  zmath  isi
    27. V. V. Ryzhikov, “Polymorphisms, Joinings, and the Tensor Simplicity of Dynamical Systems”, Funct. Anal. Appl., 31:2 (1997), 109–118  mathnet  crossref  crossref  mathscinet  zmath  isi
    28. Isabelle Lucien, “Mélange faible topologique des flots sur les surfaces”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 324:6 (1997), 669  crossref
    29. O. N. Ageev, “Dynamical systems with arbitrary spectrum multiplicity function”, Russian Math. Surveys, 53:5 (1998), 1079–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    30. O. N. Ageev, “The spectral multiplicity function and geometric representations of interval exchange transformations”, Sb. Math., 190:1 (1999), 1–28  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. A. A. Prikhod'ko, “Partitions of the phase space of a measure-preserving $\mathbb Z^d$-action into towers”, Math. Notes, 65:5 (1999), 598–609  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    32. Nataliya Chekhova, “Covering numbers of rotations”, Theoretical Computer Science, 230:1-2 (2000), 97  crossref
    33. A. A. Prikhod'ko, “Stochastic constructions of flows of rank 1”, Sb. Math., 192:12 (2001), 1799–1828  mathnet  crossref  crossref  mathscinet  zmath  isi
    34. P. ARNOUX, A. M. FISHER, “THE SCENERY FLOW FOR GEOMETRIC STRUCTURES ON THE TORUS: THE LINEAR SETTING”, Chin. Annal Math, 22:04 (2001), 427  crossref
    35. A. M. Stepin, A. M. Eremenko, “Non-unique inclusion in a flow and vast centralizer of a generic measure-preserving transformation”, Sb. Math., 195:12 (2004), 1795–1808  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    36. A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, “Nonremovable Zero Lyapunov Exponents”, Funct. Anal. Appl., 39:1 (2005), 21–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    37. Bezuglyi S. Kwiatkowski J. Medynets K., “Approximation in Ergodic Theory, Borel, and Cantor Dynamics”, Algebraic and Topological Dynamics, Contemporary Mathematics Series, 385, ed. Kolyada S. Manin Y. Ward T., Amer Mathematical Soc, 2005, 39–64  isi
    38. V. A. Kleptsyn, M. B. Nalsky, “Stability of Existence of Nonhyperbolic Measures for $C^1$-Diffeomorphisms”, Funct. Anal. Appl., 41:4 (2007), 271–283  mathnet  crossref  crossref  mathscinet  zmath  isi
    39. A. V. Kochergin, “Nondegenerate Saddle Points and the Absence of Mixing in Flows on Surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252  mathnet  crossref  mathscinet  zmath  elib  elib
    40. LORENZO J. DÍAZ, ANTON GORODETSKI, “Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes”, Ergod Th Dynam Sys, 2009, 1  crossref  isi
    41. Paul Hulse, “Counterexamples to the product rule for entropy”, Dynamical Systems, 24:1 (2009), 81  crossref
    42. Queffelec M., “The Banach Algebra M(T)”, Substitution Dynamical Systems: Spectral Analysis, Second Edition, Lecture Notes in Mathematics, 1294, 2010, 1  isi
    43. Tanja Eisner, Sophie Grivaux, “Hilbertian Jamison sequences and rigid dynamical systems”, Journal of Functional Analysis, 2011  crossref
    44. ALEXANDRE I. DANILENKO, “A survey on spectral multiplicities of ergodic actions”, Ergod. Th. Dynam. Sys, 2011, 1  crossref
    45. Ambroz P., Frid A., Masakova Z., Pelantova E., “On the number of factors in codings of three interval exchange”, Discrete Math Theor Comput Sci, 13:3 (2011), 51–66  isi
    46. Michael Boshernitzan, Jon Chaika, “Diophantine properties of IETs and general systems: quantitative proximality and connectivity”, Invent. math, 2012  crossref
    47. Giovanni Forni, “On the Brin Prize work of Artur Avila in Teichmüller dynamics and interval-exchange transformations”, JMD, 6:2 (2012), 139  crossref
    48. Kulaga-Przymus J., Parreau F., “Disjointness Properties for Cartesian Products of Weakly Mixing Systems”, Colloq. Math., 128:2 (2012), 153–177  crossref  isi
    49. D.A.hmadi Dastjerdi, M.D.abbaghian Amiri, “Rigidity in Subclasses of Transitive and Mixing Systems”, APM, 02:06 (2012), 441  crossref
    50. SŁAWOMIR SOLECKI, “Closed subgroups generated by generic measure automorphisms”, Ergod. Th. Dynam. Sys, 2013, 1  crossref
    51. A. A. Prikhod'ko, “Ergodic Automorphisms with Simple Spectrum and Rapidly Decreasing Correlations”, Math. Notes, 94:6 (2013), 968–973  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    52. Ferenczi S., “Billiards in Regular 2N-Gons and the Self-Dual Induction”, J. Lond. Math. Soc.-Second Ser., 87:3 (2013), 766–784  crossref  isi
    53. L. S. Efremova, “Dynamics of skew products of interval maps”, Russian Math. Surveys, 72:1 (2017), 101–178  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    54. Yaroslav Vorobets, “On the commutator group of the group of interval exchange transformations”, Proc. Steklov Inst. Math., 297 (2017), 285–296  mathnet  crossref  crossref  mathscinet  isi  elib
    55. I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Math. Notes, 102:6 (2017), 787–791  mathnet  crossref  crossref  isi  elib
    56. Gutman Y., Huang W., Shao S., Ye X.D., “Almost Sure Convergence of the Multiple Ergodic Average For Certain Weakly Mixing Systems”, Acta. Math. Sin.-English Ser., 34:1 (2018), 79–90  crossref  isi
    57. A. M. Vershik, P. B. Zatitskii, “Combinatorial Invariants of Metric Filtrations and Automorphisms; the Universal Adic Graph”, Funct. Anal. Appl., 52:4 (2018), 258–269  mathnet  crossref  crossref  isi  elib
    58. Forni G., Masur H., Smillie J., “Bill Veech'S Contributions to Dynamical Systems”, J. Mod. Dyn., 14 (2019), V–XXV  crossref  isi
    59. V. V. Ryzhikov, “Slabo gomoklinicheskie gruppy ergodicheskikh deistvii”, Tr. MMO, 80, no. 1, MTsNMO, M., 2019, 97–111  mathnet
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:901
    Full text:307
    References:58
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020