BIMSA > 康斯坦丁·卡宁
研究员 康斯坦丁·卡宁

团队: 概率, 应用统计和数据科学

办公室: A15-207

邮箱: khanin@bimsa.cn

研究方向: 动力系统，统计力学，概率论，遍历理论，数学物理，湍流理论

个人简介

康斯坦丁·卡宁（Konstantin Khanin）在莫斯科朗道理论物理研究所获得博士学位，并于1994年之前一直担任该所的研究员。此后，他先后在普林斯顿大学、剑桥大学艾萨克·牛顿数学科学研究所和赫瑞-瓦特大学任教，之后加入多伦多大学担任教职。 卡宁曾于2000年受邀在巴塞罗那举行的欧洲数学大会（European Congress of Mathematics）上作报告；2013年成为西蒙斯基金会（Simons Foundation）会士；2017年担任法国国际数学研究中心（CIRM）的让-莫莱（Jean-Morlet）讲席教授；2018年受邀在里约热内卢举办的国际数学家大会（ICM）上作报告。2021年，他荣获洪堡奖（Humboldt Prize，又称洪堡研究奖），以表彰其毕生在数学研究领域取得的杰出成就。

教育经历

  • - 1977      Moscow State University      Mathematics      Thesis: Gaussian Gibbs Random Fields
  • - 1983      L.D.Landau Institute for Theoretical Physics, Moscow      Mathematical Physics      Thesis: Self-averaging in Random Media      (Supervisor: Prof. Yakov Sinai)

工作经历

  • 2024 -      BIMSA      Professor
  • 2016 - 2021      Department of Mathematical and Computational Sciences, University of Toronto Mississauga      Chair
  • 2013 - 2024      Institute for Information Transmission Problems, Moscow      Leading Research Fellow
  • 2008 - 2013      Department of Mathematical and Computational Sciences, University of Toronto Mississauga      Chair
  • 2005 - 2024      Department of Mathematics, University of Toronto      Professor
  • 1999 - 2004      Isaac Newton Institute for Mathematical Sciences, University of Cambridge      Hewlett-Packard Senior Research Fellow
  • 1996 - 2005      Department of Mathematics, Heriot-Watt University, Edinburgh      Professor
  • 1994 - 1996      Department of Mathematics, Princeton University      Visiting Associate Professor
  • 1978 - 1994      L.D.Landau Institute for Theoretical Physics      Research Associate, Senior Research Fellow

出版物

  • [1] T. Hurth, K. Khanin, B. N. Lameda, On global solutions to the semidiscrete stochastic heat equation, 2025 (2025)
  • [2] D. Roy, A. Dhar, K. Khanin, M. Kulkarni, H. Spohn, Universality in coupled stochastic Burgers systems with degenerate flux Jacobian, Journal of Statistical Mechanics: Theory and Experiment, 2024(3), 033209 (2024)
  • [3] K Khanin, L Li, On the rate of convergence to coalescing Brownian motions, Annales de l'Institut Henri Poincare (B) Probabilites et statistiques, 60(1), 208-231 (2024)
  • [4] K. Khanin, L. Li, On the rate of convergence to the coalescing Brownian motions, Annales de lInstitut Henri Poincare (B), 60(1), 208-231 (2024)
  • [5] T. Hurth, K. Khanin, B. Navarro Lameda, F. Nazarov, On a factorization formula for the partition function of directed polymers, Journal of Statistical Physics, 190(10), 165 (2023)
  • [6] Yu. Bakhtin, K. Khanin, A. Mészáros, J. Voltz, Last passage percolation in a product-type random environment, arXiv preprint arXiv:2310.08379, 2024 (2023)
  • [7] K Khanin, K Zhang, L Zhang, Uniform exponential contraction for viscous Hamilton–Jacobi equations, Calculus of Variations and Partial Differential Equations, 62(3), 82 (2023)
  • [8] K. Khanin, K. Zhang, L. Zhang, Uniform exponential contraction for viscous Hamilton-Jacobi equations, Calculus of Variations and Partial Differential Equations, 62(3), 1-35 (2023)
  • [9] N. Goncharuk, K. Khanin, Yu. Kudryashov, Smooth Circle Homeomorphisms with Breaks without C2 Conjugacy, Journal of Modern Dynamics, 19, 751-772 (2023)
  • [10] N Goncharuk, K Khanin, Y Kudryashov, Circle homeomorphisms with breaks with no conjugacy., Journal of Modern Dynamics, 19 (2023)
  • [11] K. Khanin, L. Li, and Z. Yin, Point fields of last passage percolation and coalescing fractional Brownian motions, Physical Review E, 105(6), 064127 (2022)
  • [12] K Khanin, L Li, On end-point distribution for directed polymers and related problems for randomly forced Burgers equation, Philosophical Transactions of the Royal Society A, 380(2219), 20210081 (2022)
  • [13] S Ghazouani, K Khanin, The symplectic structure for renormalization of circle diffeomorphisms with breaks, Communications in Contemporary Mathematics, 24(01), 2150016 (2022)
  • [14] S. Ghazouani, K. Khanin, The symplectic structure of renormalisation of circle diffeomorphisms with breaks, Communications in Contemporary Mathematics, 24(1), 2150016-1 -- 2150016-23 (2022)
  • [15] K. Khanin, L. Li, On End-Point Distribution for Directed Polymers and Related Problems for Random Forced Burgers Equation, Philosophical Transactions of the Royal Society A, 380(2219), 1-13 (2022)
  • [16] N Goncharuk, K Khanin, Y Kudryashov, Circle homeomorphisms with breaks with no conjugacy, arXiv preprint arXiv:2112.02765 (2021)
  • [17] K Khanin, L Li, On asymptotic behavior of iterates of piecewise constant monotone maps, arXiv preprint arXiv:2110.09731 (2021)
  • [18] K. Khanin, Rigidity for circle diffeomorphisms with breaks satisfying a Zygmund smoothness condition, arXiv preprint arXiv:2107.12905, 2024 (2021)
  • [19] K. Khanin, Ya. Sinai, Mitchell Feigenbaum: Naturphilosoph and a Friend, Notices of the AMS, 68(5), 26 (2021)
  • [20] K Khanin, M Lyubich, ED Siggia, Y Sinai, Mitchell Feigenbaum, Notices of the American Mathematical Society, 68(5) (2021)
  • [21] S Gusein-Zade, Y Ilyashenko, K Khanin, S Shlosman, Y Sinai et al., ROLAND LVOVICH DOBRUSHIN (July 20, 1929-November 12, 1995), MOSCOW MATHEMATICAL JOURNAL, 20(4), 641-644 (2020)
  • [22] R Iturriaga, K Khanin, K Zhang, Exponential convergence of solutions for random Hamilton–Jacobi equations, Stochastics and Partial Differential Equations: Analysis and Computations, 8, 544-579 (2020)
  • [23] A Avila, K Khanin, M Leguil, Invariant graphs and spectral type of Schr\" odinger operators, arXiv preprint arXiv:2004.09137 (2020)
  • [24] R. Iturriaga, K. Khanin, K. Zhang, Exponential Convergence of Solutions for Random Hamilton-Jacobi Equations, Stochastics and Partial Differential Equations: Analysis and Computations, 8, 544-579 (2020)
  • [25] A. Avila, K. Khanin, M. Leguil, Invariant graphs and spectral type of Schrodinger operators, Pure and Applied Functional Analysis, 5(6), 1257-1277 (2020)
  • [26] K Khanin, S Kocić, Hausdorff dimension of invariant measure of circle diffeomorphisms with a break point, Ergodic theory and dynamical systems, 39(5), 1331-1339 (2019)
  • [27] K. Khanin, S. Kocic, Hausdorff dimension of invariant measure of circle diffeomorphisms with breaks, Ergodic Theory & Dynamical Systems, 39(5), 1331-1339 (2019)
  • [28] K. Khanin, Mathematical Physics, The Abel Prize 2013-2017, Editors H. Holden and R. Piene, 243-255 (2019)
  • [29] K. Khanin, S. Kocic, Robust local Hölder rigidity of circle maps with breaks, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 35(7), 1827-1845 (2018)
  • [30] A Habibulla, D Akhtam, K Khanin, On Linearization of Circle, Differential Equations and Dynamical Systems, 268, 1 (2018)
  • [31] Y Bakhtin, K Khanin, On global solutions of the random Hamilton–Jacobi equations and the KPZ problem, Nonlinearity, 31(4), R93 (2018)
  • [32] Yu. Bakhtin, K. Khanin, On global solutions of random Hamilton-Jacobi equations and the KPZ problem, Nonlinearity, 31, R93-R121 (2018)
  • [33] K. Khanin, Renormalization and rigidity, , 2, 1973-1993 (2018)
  • [34] AF Ismail, EYT Adesta, AHM Alam, AN Nordin, HM Salleh, A Al-Mamun et al., IIUM ENGINEERING JOURNAL, IIUM Engineering Journal, 19(1), 1 (2018)
  • [35] K Khanin, K Zhang, Hyperbolicity of minimizers and regularity of viscosity solutions for a random Hamilton–Jacobi equation, Communications in Mathematical Physics, 355, 803-837 (2017)
  • [36] H Akhadkulov, A Dzhalilov, K Khanin, Notes on a theorem of Katznelson and Ornstein, Discrete and Continuous Dynamical Systems, 37(9), 4587-4609 (2017)
  • [37] H. Akhadkulov, A. Dzhalilov, K. Khanin, On linearization of circle diffeomorphisms, , 1-8 (2017)
  • [38] EB Vul, YG Sinai, KM Khanin, Feigenbaum universality and the thermodynamic formalism, Universality in Chaos, 491-530 (2017)
  • [39] K. Khanin, S. Kocic, On the smoothness of the conjugacy between circle maps with a break, Proceedings of the Steklov Institute of Mathematics, 297, 200-207 (2017)
  • [40] K. Khanin, Mathematical Journey of Yakov Sinai, Journal of Statistical Physics, 166(3), 463-466 (2017)
  • [41] K. Khanin, S. Kocic, E. Mazzeo, C1-rigidity of circle diffeomorphisms with breaks for almost all rotation numbers, Ann. Sci. Ec. Norm. Super., 50, 1163-1203 (2017)
  • [42] K. Khanin, S. Kocic, Rigidity for a class of generalized interval exchange transformations, Contemp. Math, 698, 16-26 (2017)
  • [43] H. Akhadkulov, A. Dzhalilov, K. Khanin, Note on a theorem of Katznelson and Ornstein, Discrete and Continuous Dynamical Systems- Series A, 37(9), 4587-4609 (2017)
  • [44] K. Khanin, K. Zhang, Hyperbolicity of Minimizers and Regularity of Viscosity Solutions for Random Hamilton-Jacobi Equation, Comm Math Physics, 355, 803-837 (2017)
  • [45] K Khanin, S Kocic, E Mazzeo, C^1 -rigidity of circle diffeomorphisms with breaks for almost all rotation numbers, Ann. Sci. Ec. Norm. Sup´er. ´, 50, 1163-1203 (2017)
  • [46] K Khanin, A Sobolevski, On dynamics of Lagrangian trajectories for Hamilton–Jacobi equations, Archive for Rational Mechanics and Analysis, 219(2), 861-885 (2016)
  • [47] K. Khanin, A. Sobolevski, On Dynamics of Lagrangian Trajectories for Hamilton-Jacobi Equations, Archive for Rational Mechanics and Analysis, 219(2), 861-885 (2016)
  • [48] K. Khanin, S. Kocic, Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks, Geometric and Functional Analysis, 24(6), 2002-2028 (2014)
  • [49] A. Bufetov, B. Gurevich, K. Khanin, F. Cellarosi, The Abel Prize award to Ya. G. Sinai, , 69(5), 931 (2014)
  • [50] T Alberts, K Khanin, J Quastel, The intermediate disorder regime for directed polymers in dimension$1+1$, 42(3), 1212-1256 (2014)
  • [51] Yu. Bakhtin, E. Cator, K. Khanin, Space-time stationary solutions for the Burgers equation, Journal of the American Mathematical Society, 27(1), 193-238 (2014)
  • [52] T. Alberts, K. Khanin, J. Quastel, The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1, Annals of Probability, 42(3), 1212-1256 (2014)
  • [53] T. Alberts, K. Khanin, J. Quastel, The continuum directed random polymer, Journal of Statistical Physics, 154(1), 305-326 (2014)
  • [54] K. Khanin, M. Yampolsky, Hyperbolicity of renormalization of circle maps with a break-type singularity, arXiv preprint arXiv:1312.4184, 15, 107-121 (2013)
  • [55] K Khanin, A Teplinsky, Renormalization horseshoe and rigidity for circle diffeomorphisms with breaks, Communications in Mathematical Physics, 320, 347-377 (2013)
  • [56] K Khanin, S Kocić, Absence of robust rigidity for circle maps with breaks, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 30(3), 385-399 (2013)
  • [57] K Konstantin, Y Tatiana, Ergodic properties of random billiards driven by thermostats, Communications in Mathematical Physics, 320(1), 121-147 (2013)
  • [58] A Boritchev, K Khanin, On the hyperbolicity of minimizers for 1D random Lagrangian systems, Nonlinearity, 26(1), 65 (2012)
  • [59] A Grigo, K Khanin, D Szasz, Mixing rates of particle systems with energy exchange, Nonlinearity, 25(8), 2349 (2012)
  • [60] K Khanin, Intermediate Disorder Regime for Directed Polymers and KPZ Scalings, The Nature of Turbulence, 34 (2011)
  • [61] K Khanin, S Nechaev, G Oshanin, A Sobolevski, O Vasilyev, Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 82(6), 061107 (2010)
  • [62] OY Teplins’ kyi, KM Khanin, Smooth conjugacy of circle diffeomorphisms with break, Nonlinear Oscillations, 13(1), 112-127 (2010)
  • [63] T Alberts, K Khanin, J Quastel, Intermediate Disorder Regime for Directed Polymers in Dimension$1+1$, Physical review letters, 105(9), 090603 (2010)
  • [64] K Khanin, S Koci, Examples of non-rigidity for circle homeomorphisms with breaks, (2010)
  • [65] K Khanin, A Sobolevski, Particle dynamics inside shocks in Hamilton–Jacobi equations, Philosophical Transactions of the Royal Society A: Mathematical, Physical …, 368(1916), 1579-1593 (2010)
  • [66] P Bachurin, K Khanin, J Marklof, A Plakhov, Perfect retroreflectors and billiard dynamics, arXiv preprint arXiv:0911.1984 (2009)
  • [67] K Khanin, A Teplinsky, Herman’s theory revisited, Inventiones mathematicae, 178, 333-344 (2009)
  • [68] Y Bakhtin, K Khanin, Localization and Perron--Frobenius theory for directed polymers, arXiv preprint arXiv:0909.2293 (2009)
  • [69] B Fayad, K Khanin, Smooth Linearization of Commuting Circle Diffeomorphisms, Annals of Mathematics, 170(2), 960-981 (2009)
  • [70] P BACHURIN, K KHANIN, J MARKLOF, A PLAKHOV, EXITS FROM A SEMI-INFINITE TUBE, preparation (2007)
  • [71] J Bec, K Khanin, Burgers turbulence, Physics reports 447 (1-2), 1-66 (2007)
  • [72] K Khanin, A Teplinsky, Robust rigidity for circle diffeomorphisms with singularities, Inventiones mathematicae, 169(1), 193-218 (2007)
  • [73] K Khanin, JL Dias, J Marklof, Multidimensional continued fractions, dynamical renormalization and KAM theory, Communications in mathematical physics, 270(1), 197-231 (2007)
  • [74] K Khanin, JL Dias, J Marklof, Renormalization of multidimensional Hamiltonian flows, Nonlinearity, 19(12), 2727 (2006)
  • [75] U Frisch, K Khanin, T Matsumoto, Multifractality of the Feigenbaum attractor and fractional derivatives, Journal of statistical physics, 121, 671-695 (2005)
  • [76] D Gomes, R Iturriaga, K Khanin, P Padilla, Viscosity limit of stationary distributions for the random forced Burgers equation, Mosc. Math. J, 5(3), 613-631 (2005)
  • [77] KM Khanin, DV Khmelev, AN Sobolevski, On the velocities of Lagrangian minimizers, Moscow Mathematical Journal, 5(1), 157-169 (2005)
  • [78] YS Ilyashenko, KM Khanin, S Shlosman, MA Tsfasman, Yakov G. Sinai, Moscow Mathematical Journal, 5(3), 497-498 (2005)
  • [79] AY Teplinskii, KM Khanin, Rigidity for circle diffeomorphisms with singularities, Russian Mathematical Surveys, 59(2) (2004)
  • [80] K Khanin, D Khmelev, A Sobolevskii, A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain, arXiv preprint math/0312395 (2003)
  • [81] J Bec, K Khanin, Forced Burgers equation in an unbounded domain, Journal of statistical physics, 113, 741-759 (2003)
  • [82] K Khanin, D Khmelev, Renormalizations and rigidity theory for circle homeomorphisms with singularities of the break type, Communications in mathematical physics, 235, 69-124 (2003)
  • [83] VH Hoang, K Khanin, Random Burgers equation and Lagrangian systems in non-compact domains, Nonlinearity, 16(3), 819 (2003)
  • [84] R Iturriaga, K Khanin, Burgers turbulence and random Lagrangian systems, Communications in Mathematical Physics, 232, 377-428 (2003)
  • [85] D Gomes, R Iturriaga, K Khanin, P Padilla, Convergence of viscosity solutions of Burgers equation with random forcing, Preprint (2003)
  • [86] AVVIOA Rybko, KM Khanin, DV Khmelev, A Nonlinear Generalization of Perron's theorem, Doklady Mathematics, 67(2), 221-225 (2003)
  • [87] LG Fel, KM Khanin, On Effective Conductivity on ℤLattice, Journal of statistical physics, 108, 1015-1031 (2002)
  • [88] J Bec, R Iturriaga, K Khanin, Topological shocks in Burgers turbulence, Physical review letters, 89(2), 024501 (2002)
  • [89] DM Hardcastle, K Khanin, The d-dimensional Gauss transformation: strong convergence and Lyapunov exponents, Experimental Mathematics, 11(1), 119-129 (2002)
  • [90] K Khanin, D Khmelev, A Rybko, A Vladimirov, Steady solutions for FIFO networks, Moscow mathematical journal, 1(3), 407-419 (2001)
  • [91] J Bec, U Frisch, K Khanin, B Villone, A universal law for tails of density pdf's in multi-dimensional Burgers turbulence, arXiv preprint astro-ph/0101298 (2001)
  • [92] K Khanin, R Khanin, A probabilistic model for the establishment of neuron polarity, Journal of Mathematical Biology, 42, 26-40 (2001)
  • [93] DM Hardcastle, K Khanin, Continued fractions and the d-dimensional Gauss transformation, Communications in Mathematical Physics, 215, 487-515 (2001)
  • [94] R Iturriaga, K Khanin, Burgers turbulence and dynamical systems, European Congress of Mathematics, 1, 429-443 (2001)
  • [95] JL Lebowitz, K Khanin, E Wienan, V Yakhot, G Gallavotti, H van Beijeren, Program of the 84th Statistical Mechanics Meeting, Journal of Statistical Physics, 103(5/6) (2001)
  • [96] DM Hardcastle, K Khanin, On almost everywhere strong convergence of multi-dimensional continued fraction algorithms, Ergodic Theory and Dynamical Systems, 20(6), 1711-1733 (2000)
  • [97] J Bec, U Frisch, K Khanin, Kicked burgers turbulence, Journal of Fluid Mechanics, 416, 239-267 (2000)
  • [98] K Khanin, A Mazel, Invariant measures for Burgers equation with stochastic forcing, Annals of mathematics, 151(3), 877-960 (2000)
  • [99] DM Hardcastle, K Khanin, MR1804954 (2001k: 11151) 11K50, Ergodic Theory Dynam. Systems, 20(6), 1711-1733 (2000)
  • [100] K Khanin, Burgers Equation with Random Force, Proceedings of the XII International Congress in Mathematical Physics (1999)
  • [101] AA Dzhalilov, KM Khanin, On an invariant measure for homeomorphisms of a circle with a point of break, Functional Analysis and its Applications, 32(3), 153-161 (1998)
  • [102] E Weinan, K Khanin, A Mazel, Y Sinai, Probability distribution functions for the random forced Burgers equation, Physical review letters, 78(10), 1904 (1997)
  • [103] KM Khanin, Rigidity for circle homeomorphisms with a break-type singularity, Doklady Mathematics, 56(3), 859-861 (1997)
  • [104] K Khanin, Rigidity for Circle Homeomorphisms with Break Singularity, Physics-Doklady, 56, 859-861 (1997)
  • [105] K Khanin, Y Sinai, Hyperbolicity of minimizing trajectories for two-dimensional Hamiltonian systems with random forcing, Proceedings of the Steklov Institute of Mathematics, 216, 169-174 (1997)
  • [106] AA Dzhalilov, KM Khanin, On an invariant measure for homeomorphisms of the circle with a single break point, Russian Mathematical Surveys, 51(6), 1198 (1996)
  • [107] BR Hunt, KM Khanin, YG Sinai, JA Yorke, Fractal properties of critical invariant curves, Journal of statistical physics, 85, 261-276 (1996)
  • [108] SP Novikov, LA Bunimovich, AM Vershik, BM Gurevich, EI Dinaburg et al., Yakov Grigor'evich Sinai (on his sixtieth birthday), Russian Mathematical Surveys, 51(4), 765 (1996)
  • [109] KM Khanin, Mixing for area-preserving flows on the two-dimensional torus, International Journal of Modern Physics B, 10(18), 2167-2188 (1996)
  • [110] KM Khanin, Random walks in a random potential: loop condensation effects, International Journal of Modern Physics B, 10(18), 2393-2404 (1996)
  • [111] KM Khanin, Rigidity in one-dimensional dynamics, International Journal of Modern Physics B, 10(18), 2311-2324 (1996)
  • [112] EB Vul, YG Sinai, KM Khanin, Feigenbaum universality and the thermodynamic, 30 Years of the Landau Institute: Selected Papers, 11(3), 389 (1996)
  • [113] BR Hunt, KM Khanin, Yakov G. Sinai 2; 3, and James A. Yorke December 31, 1995, (1995)
  • [114] K Khanin, Y Kifer, Thermodynamic formalism for random transformations and statistical mechanics, American Mathematical Society Translations: Series 2, 107-140 (1995)
  • [115] KM Khanin, JL Lebowitz, AE Mazel, YG Sinai, Self-avoiding walks in five or more dimensions: polymer expansion approach, Russian Mathematical Surveys, 50(2), 403 (1995)
  • [116] KM Khanin, AE Mazel, SB Shlosman, YG Sinai, Loop condensation effects in the behavior of random walks, The Dynkin Festschrift: Markov Processes and their Applications, 167-184 (1994)
  • [117] YG Sinai, KM Khanin, Mixing for some classes of special flows over rotations of the circle, Functional Analysis and Its Applications, 26(3), 155-169 (1992)
  • [118] KM Khanin, YG Sinai, Mixing of some classes of special flows over rotations of the circle, Funct. Anal. Appl, 26(3), 155-169 (1992)
  • [119] EM Lifshitz, IM Khalatnikov, YG Sinai, KM Khanin, LN Shchur, On the stochastic properties of relativistic cosmological models near the singularity, Perspectives in Theoretical Physics, 731-735 (1992)
  • [120] YG Sinai, KM Khanin, Mixing for certain classes of special flows over the circle shift, Func, Anal. and Appl, 26, 155 (1992)
  • [121] KM Khanin, Universal estimates for critical circle mappings., Chaos (Woodbury, NY), 1(2), 181-186 (1991)
  • [122] KM Khanin, EB Vul, Circle homeomorphisms with weak discontinuities, Advances in Sov. Math, 3, 57-98 (1991)
  • [123] ВА Гурвич, КМ Ханин, Распределение Пуассона для количества пар близких точек, Доклады Академии наук, 316(3), 533-538 (1991)
  • [124] VA Gurvich, KM Khanin, The Gaussian distribution for sums of distances, Doklady Akademii Nauk, 316(2), 279-284 (1991)
  • [125] EB Vul, KM Khanin, Homeomorphisms of the circle with singularities of “break” type, Russian Mathematical Surveys, 45(3), 229 (1990)
  • [126] K Khanin, Thermodynamic formalism for critical circle mappings, Chaos, 71-90 (1990)
  • [127] YG Sinai, KM Khanin, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Russian Mathematical Surveys, 44(1) (1989)
  • [128] YG Sinai, KM Khanin, Renormalization group method in the theory of dynamical systems, Int. J. Mod. Phys. B;(United States), 2(2) (1988)
  • [129] VM Kharlamov, AN Varchenko, VM Petkov, YG Sinai, KM Khanin et al., Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics (September, 30–December, 9, 1987), Uspekhi Matematicheskikh Nauk, 43(3), 239-245 (1988)
  • [130] AI Gol'berg, VA Gurvich, MY Rozenblyum, KM Khanin, The conditions of solubility by domination of concave n-person games, Russian Mathematical Surveys, 42(2), 277 (1987)
  • [131] KM Khanin, YG Sinai, A new proof of M. Herman's theorem, Communications in Mathematical Physics, 112, 89-101 (1987)
  • [132] K Khanin, YG Sinai, The renormalization group method and Kolmogorov-Arnold-Moser theory, Nonlinear phenomena in plasma physics and hydrodynamics, 31-64 (1986)
  • [133] IG Sinai, KM Khanin, LH Shchur, A new approach to the plotting of fixed points of renormalization groups in dynamic systems, Radiofizika, 29(9), 1061-1066 (1986)
  • [134] YG SINAJ, KM KHANIN, LN SHUR, A NEW APPROACH TO THE CONSTRUCTION OF FIXED-POINTS OF RENORMALIZATION-GROUP TRANSFORMATIONS IN DYNAMIC-SYSTEMS, IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII RADIOFIZIKA, 29(9), 1061-1066 (1986)
  • [135] IM Khalatnikov, EM Lifshitz, KM Khanin, LN Shchur, YG Sinai, On the stochasticity in relativistic cosmology, Journal of statistical physics, 38, 97-114 (1985)
  • [136] EM Lifshits, IM Khalatnikov, YG Sinaj, KM Khanin, LN Shchur, Stochastic properties of relativistic cosmological models near a singularity, Pis' ma Zh. Eksp. Teor. Fiz.;(USSR), 38(2) (1983)
  • [137] AI Gol'berg, YG Sinai, KM Khanin, Universal properties for sequences of bifurcations of period three, Russian Mathematical Surveys, 38(1) (1983)
  • [138] AI Golberg, YG Sinai, KM Khanin, Universal properties of the period-tripling sequence, Usp. Mat. Nauk, 38, 159-160 (1983)
  • [139] EB Vul, KM Khanin, The unstable separatrix of Feigenbaum's fixed-point, Russian Mathematical Surveys, 37(5), 200 (1982)
  • [140] VV Anshelevich, KM Khanin, YG Sinai, Symmetric random walks in random environments, Communications in Mathematical Physics, 85, 449-470 (1982)
  • [141] KM Khanin, Quasi-periodic motions of vortex systems, Physica D: Nonlinear Phenomena, 4(2), 261-269 (1982)
  • [142] KM Khanin, The existence of conditionally periodic motions for a system of plane vortices, Russian Mathematical Surveys, 36(1), 234 (1981)
  • [143] KM Khanin, Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian, Teoreticheskaya i Matematicheskaya Fizika, 43(2), 253-260 (1980)
  • [144] KM Khanin, YG Sinai, Existence of free energy for models with long-range random Hamiltonians, Journal of Statistical Physics, 20(6), 573-584 (1979)
  • [145] TN Bakiev, AI Bufetov, VA Vassiliev, SM Voronin, AA Glutsyuk, ..., On the 80th birthday of Yulij Sergeevich Ilyashenko, Uspekhi Matematicheskikh Nauk, 80(2), 171-183 (2025)
  • [146] T Matsumoto, D Roy, K Khanin, R Pandit, U Frisch, Large-scale multifractality and lack of self-similar decay for Burgers and three-dimensional Navier–Stokes turbulence, Journal of Fluid Mechanics, 1016, A51 (2025)
  • [147] T Matsumoto, D Roy, K Khanin, R Pandit, U Frisch, Large-scale multifractality and lack of self-similar decay for Burgers and 3D Navier-Stokes turbulence, arXiv (2025)
  • [148] AY Teplinskii, KM Khanin, A sharp estimate for the smoothness of a conjugacy linearizing a nonlinear circle diffeomorphism, Doklady Mathematics, 80(2), 701-705 (2009)
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更新时间: 2026-03-10 18:00:06