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Uspekhi Mat. Nauk, 1989, Volume 44, Issue 1(265), Pages 57–82 (Mi umn1965)  

This article is cited in 38 scientific papers (total in 40 papers)

Smoothness of conjugacies of diffeomorphisms of the circle with rotations

Ya. G. Sinai, K. M. Khanin


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English version:
Russian Mathematical Surveys, 1989, 44:1, 69–99

Bibliographic databases:

UDC: 517.5
MSC: 37C05, 37C40
Received: 10.01.1988

Citation: Ya. G. Sinai, K. M. Khanin, “Smoothness of conjugacies of diffeomorphisms of the circle with rotations”, Uspekhi Mat. Nauk, 44:1(265) (1989), 57–82; Russian Math. Surveys, 44:1 (1989), 69–99

Citation in format AMSBIB
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\pages 57--82
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\yr 1989
\vol 44
\issue 1
\pages 69--99
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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. E. B. Vul, K. M. Khanin, “Homeomorphisms of the circle with singularities of “break” type”, Russian Math. Surveys, 45:3 (1990), 229–230  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Ya. G. Sinai, K. M. Khanin, “Mixing for some classes of special flows over rotations of the circle”, Funct. Anal. Appl., 26:3 (1992), 155–169  mathnet  crossref  mathscinet  zmath
    3. D. V. Kosygin, A. A. Minasov, Ya. G. Sinai, “Statistical properties of the spectra of Laplace–Beltrami operators on Liouville surfaces”, Russian Math. Surveys, 48:4 (1993), 1–142  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. I. Veitsblit, “Renormalization of Diffeomorphisms of the Circle and Scaling of “Arnold Tongues””, Funct. Anal. Appl., 29:3 (1995), 194–196  mathnet  crossref  mathscinet  zmath  isi
    5. S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. S. Kh. Aranson, E. V. Zhuzhoma, V. S. Medvedev, “Strengthening the $C^r$-closing lemma for dynamical systems and foliations on the torus”, Math. Notes, 61:3 (1997), 265–271  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. A. A. Dzhalilov, K. M. Khanin, “On an Invariant Measure for Homeomorphisms of a Circle with a Point of Break”, Funct. Anal. Appl., 32:3 (1998), 153–161  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. A. Dzhalilov, “The Hölder property of singular invariant measures of circle homeomorphisms with single corners”, Theoret. and Math. Phys., 121:3 (1999), 1557–1566  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. A. Dzhalilov, “Piecewise smoothness of conjugate homeomorphisms of a circle with corners”, Theoret. and Math. Phys., 120:2 (1999), 961–972  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. A. A. Dzhalilov, “Singular invariant measures of homeomorphisms of the circle with break points”, Russian Math. Surveys, 54:4 (1999), 841–842  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. A. Yu. Teplinskii, K. M. Khanin, “Rigidity for circle diffeomorphisms with singularities”, Russian Math. Surveys, 59:2 (2004), 329–353  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Weigu Li, Kening Lu, “Sternberg theorems for random dynamical systems”, Comm Pure Appl Math, 58:7 (2005), 941  crossref  mathscinet  zmath  isi
    13. Akhtam Dzhalilov, Isabelle Liousse, “Circle homeomorphisms with two break points”, Nonlinearity, 19:8 (2006), 1951  crossref  mathscinet  zmath  isi
    14. Voutaz E., “Hyperbolicity of the Renormalization Operator for Critical C-R Circle Mappings”, Ergod. Theory Dyn. Syst., 26:Part 2 (2006), 585–618  crossref  isi
    15. 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
    16. Diaz-Espinosa, O, “Renormalization and central limit theorem for critical dynamical systems with weak external noise”, Journal of Modern Dynamics, 1:3 (2007), 477  mathscinet  zmath  isi
    17. Bassam Fayad, Kostantin Khanin, “Smooth linearization of commuting circle diffeomorphisms”, Ann of Math, 170:2 (2009), 961  crossref  mathscinet  zmath  isi
    18. Teplinskii A.Yu., Khanin K.M., “A sharp estimate for the smoothness of a conjugacy linearizing a nonlinear circle diffeomorphism”, Dokl. Math., 80:2 (2009), 701–705  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    19. Dzhalilov A., Akin H., Temir S., “Conjugations between circle maps with a single break point”, Journal of Mathematical Analysis and Applications, 366:1 (2010), 1–10  crossref  mathscinet  zmath  isi
    20. Teplins'kyi O.Yu., Khanin K.M., “Smooth Conjugacy of Circle Diffeomorphisms With Break”, Nonlinear Oscillations, 13:1 (2010), 112–127  crossref  isi
    21. A. A. Dzhalilov, D. Mayer, U. A. Safarov, “Piecewise-smooth circle homeomorphisms with several break points”, Izv. Math., 76:1 (2012), 94–112  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. Renato Calleja, Jordi-Lluís Figueras, “Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map”, Chaos, 22:3 (2012), 033114  crossref
    23. Habibulla Akhadkulov, Mohd Salmi Md Noorani, “On Absolute Continuity of Conjugations between Circle Maps with Break Points”, Abstract and Applied Analysis, 2012 (2012), 1  crossref
    24. HABIBULLA AKHADKULOV, AKHTAM DZHALILOV, DIETER MAYER, “On conjugations of circle homeomorphisms with two break points”, Ergod. Th. Dynam. Sys, 2012, 1  crossref
    25. ABDELHAMID ADOUANI, HABIB MARZOUGUI, “Singular measures for class P-circle homeomorphisms with several break points”, Ergod. Th. Dynam. Sys, 2012, 1  crossref
    26. Abdelhamid Adouani, Habib Marzougui, “On piecewise smoothness of conjugacy of classPcircle homeomorphisms to diffeomorphisms and rotations”, Dynamical Systems, 27:2 (2012), 169  crossref
    27. Habibulla Akhadkulov, M.S.a.M.d Noorani, Akhtam Dzhalilov, “On Invariant Measure of the Circle Maps”, J. Phys.: Conf. Ser, 435 (2013), 012011  crossref
    28. Calleja R.C. Celletti A. de la Llave R., “A Kam Theory for Conformally Symplectic Systems: Efficient Algorithms and their Validation”, J. Differ. Equ., 255:5 (2013), 978–1049  crossref  isi
    29. Habibulla Akhadkulov, Akhtam Dzhalilov, M.S.almi Md Noorani, “On conjugacies between piecewise-smooth circle maps”, Nonlinear Analysis: Theory, Methods & Applications, 99 (2014), 1  crossref
    30. Akhtam Dzhalilov, M.S.almi Md Noorani, Sokhobiddin Akhatkulov, “On Critical Circle Homeomorphisms with Infinite Number of Break Points”, Abstract and Applied Analysis, 2014 (2014), 1  crossref
    31. Habibulla Akhadkulov, M.S.a.M.d Noorani, “On conjugations of -homeomorphisms”, Indagationes Mathematicae, 2014  crossref
    32. Abdumajid Begmatov, Akhtam Dzhalilov, Dieter Mayer, “Renormalizations of circle hoemomorphisms with a single break point”, DCDS-A, 34:11 (2014), 4487  crossref
    33. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    34. Akhatkulov S., Noorani Mohd Salmi Md, Akhadkulov H., “On Conjugacies of Circle Maps With Singular Points”, Statistics and Operational Research International Conference, AIP Conference Proceedings, 1613, eds. Shitan M., Lee L., Eshkuvatov Z., Amer Inst Physics, 2014, 266–274  crossref  isi
    35. Akhadkulov H., Noorani Mohd Salmi Md, Akhatkulov S., “On Smoothness of Conjugations Between Break Equivalent Circle Maps”, Proceedings of the 3rd International Conference on Mathematical Sciences, AIP Conference Proceedings, 1602, eds. Zin W., DzulKifli S., Razak F., Ishak A., Amer Inst Physics, 2014, 749–753  crossref  isi
    36. Akhtam Dzhalilov, Dieter Mayer, Utkir Safarov, “On the conjugation of piecewise smooth circle homeomorphisms with a finite number of break points”, Nonlinearity, 28:7 (2015), 2441  crossref
    37. ABDELHAMID ADOUANI, “Conjugation between circle maps with several break points”, Ergod. Th. Dynam. Sys, 2015, 1  crossref
    38. Akhatkulov S. Noorani Mohd. Salmi Md. Akhadkulov H., “On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class”, J. Nonlinear Sci. Appl., 10:1 (2017), 48–59  crossref  mathscinet  isi
    39. Konstantin Khanin, Saša Kocić, “On the smoothness of the conjugacy between circle maps with a break”, Proc. Steklov Inst. Math., 297 (2017), 200–207  mathnet  crossref  crossref  mathscinet  isi  elib
    40. Akhatkulov S. Noorani Mohd Salmi Md, “On the Singularity of the Conjugation Between Piecewise-Smooth Circle Homeomorphisms”, Bull. Malays. Math. Sci. Soc., 41:3 (2018), 1607–1622  crossref  isi
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