Russian Academy of Sciences

Landau Institute for Theoretical Physics

Konstantin M. Khanin

Researcher (associated)

Ph. D.

Email:

Publications

    1. K. Khanin, Mathematical Journey of Yakov Sinai, J. Stat. Phys. 166, 463-466 (2017).
    2. K. Khanin, Particle Dynamics Inside Shocks in Hamilton–Jacobi Equations, AIP Conf. Proc. 1389, 690-692 (2011), Scopus: 2-s2.0-81855176339.
    3. A.Yu. Teplinskii, K.M. Khanin, Gladkoe sopryazhenie diffeomorfizmov kruga s izlomom, Nelіnіinі kolivannya, 13(1), 100-114 (2010) [O.Yu. Teplins’kyi, K.M. Khanin, Smooth conjugacy of circle diffeomorphisms with break, Nonlinear Oscillations, 13(1), 112-127 (2010)], Scopus: 2-s2.0-81955167666.
    4. B. Fayad, K. Khanin, Smooth linearization of commuting circle diffeomorphisms, Ann. Math., 170(2), 961-980 (2009); math/0605214.
    5. K. Khanin, A. Teplinsky, Herman's Theory Revisited, Invent. Math. 178(2), 333-344 (2009); arXiv:0707.0075.
    6. A.Yu. Teplinskii, K.M. Khanin, Tochnaya otsenka gladkosti sopryazheniya, linearizuyushchego nelineinyi diffeomorfizm okruzhnosti, Dokl. Akad. nauk, 428(3), 317–321 (2009) [A.Yu. Teplinskii, K.M. Khanin, A sharp estimate for the smoothness of a conjugacy linearizing a nonlinear circle diffeomorphism, Dokl. Math., 80(2), 701-705 (2009)].
    7. K. Khanin, J. Lopes Dias, J. Marklof, Multidimensional continued fractions, dynamical renormalization and KAM theory, Commun. Math. Phys., 270 (1), 197-231 (2007); math-ph/0509007.
    8. K. Khanin, A. Teplinsky, Robust rigidity for circle diffeomorphisms with singularities, Invent. Math., 169(1), 193-218 (2007).
    9. J. Beca, K. Khanin, Burgers turbulence, Physics Reports, 447(1-2), 1-66 (2007); arXiv:0704.1611.
    10. K. Khanin, J. Lopes Dias, J. Marklof, Renormalization of multidimensional Hamiltonian flows, Nonlinearity, 19(12), 2727-2753 (2006).
    11. U. Frisch, K. Khanin, T. Matsumoto, Multifractality of the Feigenbaum attractor and fractional derivatives, J. Stat. Phys., 121 (5-6), 671-695 (2005); nlin/0309068.
    12. K.M. Khanin, D.V. Khmelev, A.N. Sobolevskii, On the Velocities of Lagrangian Minimizers, Moscow Math. J., 5(1), 157-169 (2005).
    13. D. Gomes, R. Iturriaga, K.M. Khanin, P. Padilla, Viscosity limit of stationary distributions for the random forced Burgers equation, Moscow Math. J., 5(3), 613-631 (2005).
    14. K. Khanin, D. Khmelev, A. Sobolevskii, A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain, Contemporary Mathematics, 377, 161-179 (2005) [Idempotent Mathematics and Mathematical Physics. Proc. Int. Workshop, Vienna, Austria, Feb. 3-10, 2003. Ed. by G.L. Litvinov, V.P. Maslov. AMS, Providence, 2005, ISBN 0-8218-3538-6]; math/0312395.
    15. Yu.S. Ilyashenko, K.M. Khanin, S. Shlosman, M.A. Tsfasman, Yakov G. Sinai, Moscow Math. J., 5(3), 497–498 (2005).
    16. A.Yu. Teplinskii, K.M. Khanin, Zhestkost’ dlya diffeomorfizmov okruzhnosti s osobennostyami, Uspekhi mat. nauk, 59:2(356), 137–160 (2004) [A.Yu. Teplinskii, K.M. Khanin, Rigidity for circle diffeomorphisms with singularities, Russ. Math. Surv., 59(2), 329-353 (2004)].
    17. R. Iturriaga, K. Khanin, Burgers turbulence and random Lagrangian systems, Commun. Math. Phys., 232 (3), 377-428 (2003).
    18. K. Khanin, D. Khmelev, Renormalizations and rigidity theory for circle homeomorphisms with singularities of the break type, Commun. Math. Phys., 235 (1), 69-124 (2003).
    19. J. Bec, K. Khanin, Forced Burgers Equation in an Unbounded Domain, J. Stat. Phys. 113(5-6), 741-759 (2003); nlin/0210001.
    20. Viet Ha Hoang, K. Khanin, Random Burgers equation and Lagrangian systems in non-compact domains, Nonlinearity, 16(3), 819-842 (2003).
    21. A.A. Vladimirov, V.I. Oseledets, A.N. Rybko, K.M. Khanin, D.V. Khmelyov, Nelineinoe obobshchenie teoremy Perrona, Dokl. Akad. nauk, 389(4), 452-456 (2003) [A.A. Vladimirov, V.I. Oseledets, A.N. Rybko, K.M. Khanin, D.V. Khmelev, A nonlinear generalization of Perron's theorem, Dokl. Math., 67 (2), 221-225 (2003)].
    22. D.M. Hardcastle, K. Khanin, The d-dimensional Gauss transformation: strong convergence and Lyapunov exponents, Exp. Math. 11(1), 119-129 (2002).
    23. L.G. Fel, K.M. Khanin, On Effective Conductivity on ${\mathbb Z}^d$ Lattice, J. Stat. Phys., 108 (5-6), 1015-1031 (2002); math-ph/0111048.
    24. J. Bec, R. Iturriaga, K. Khanin, Topological shocks in Burgers turbulence, Phys. Rev. Lett. 89, 024501 (2002); nlin/0112050.
    25. D.M. Hardcastle, K. Khanin, Continued fractions and the d-dimensional Gauss transformation, Commun. Math. Phys., 215 (3), 487-515 (2001).
    26. K. Khanin, R. Khanin, A probabilistic model for the establishment of neuron polarity, J. Math. Biol., 42 (1), 26-40 (2001).
    27. K. Khanin, D. Khmelev, A. Rybko, A. Vladimirov, Steady Solutions for FIFO Networks, Moscow Math. J., 1(3), 407-419 (2001).
    28. R. Iturriaga, K. Khanin, Burgers turbulence and dynamical systems, Prog. Math. 201, 429-443 (2001) [Proc. 3rd European Congress of Mathematics, Barcelona, Spain, 2000. Vol. I. Boston-Basel-Berlin: Birkhauser, 2001].
    29. Weinan E., K. Khanin, A. Mazel, Ya. Sinai, Invariant measures for Burgers equation with stochastic forcing, Ann. Math., 151 (3), 877-960 (2000); math/0005306.
    30. D.M. Hardcastle, K. Khanin, On almost everywhere strong convergence of multi-dimensional continued fraction algorithms, Ergodic Theory and Dynamical Systems, 20 (6), 1711-1733 (2000).
    31. J. Bec, U. Frisch, K. Khanin, Kicked Burgers turbulence, J. Fluid Mech., 416, 239-267 (2000); chao-dyn/9910001.
    32. J. Bec, U. Frisch, K. Khanin, B. Villone, A universal law for tails of density pdf's in multi-dimensional Burgers turbulence, Advances in Turbulence VIII, C. Dopazo et al., eds., CIMNE, Barcelona, 2000; astro-ph/0101298.
    33. A.A. Dzhalilov, K.M. Khanin, Ob invariantnoi mere dlya gomeomorfizmov okruzhnosti s izlomom, Funkts. analiz i ego pril., 32(3), 11–21 (1998) [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), 153-161 (1998)].
    34. K.M. Khanin, Burgers Equation with Random Force, Proc. XII Int. Congress in Mathematical Physics (ICM'97), Brisbane, July 13-17, 1997. Ed. by David Dewitt, Mark Gould, Paul A. Pearce, Anthony J. Bracken. International Press of Boston, 1998. ISBN: 978-1571460554.
    35. E. Weinan, K. Khanin, A. Mazel, Y. Sinai, Probability distribution functions for the random forced burgers equation, Phys. Rev. Lett. 78(10), 1904-1907 (1997), WoS: A1997WM06400019.
    36. K. Khanin, Zhestkost’ dlya gomeomorfizmov okruzhnosti s osobennostyami tipa izloma, Dokl. Akad. nauk, 357 (2), 176-179 (1997) [K.M. Khanin, Rigidity for circle homeomorphisms with break singularities, Dokl. Math. 56(3), 859-861 (1997)].
    37. Ya.G. Sinai, K.M. Khanin, Giperbolichnost’ minimiziruyushchikh traektorii dlya dvumernykh gamil’tonovykh sistem so sluchainoi siloi, Tr. MIAN, 216 (Dinamicheskie sistemy i smezhnye voprosy, Sb. statei. K 60-letiyu so dnya rozhdeniya akad. Dmitriya Viktorovicha Anosova), 176-180 (1997) [Ya. Sinai, K. Khanin, Hyperbolicity of Minimizing Trajectories for Two-Dimensional Hamiltonian Systems with Random Forcing, Proc. Steklov Inst. Math., 216, 169-173 (1997)].
    38. K.M. Khanin, Mixing for area-preserving flows on the two-dimensional torus, Int. J. Mod. Phys. B 10(18-19), 2167-2188 (1996).
    39. K.M. Khanin, Rigidity in one-dimensional dynamics, Int. J. Mod. Phys. B 10(18-19), 2311-2324 (1996).
    40. K.M. Khanin, Random walks in a random potential: Loop condensation effects, Int. J. Mod. Phys. B 10(18-19), 2393-2404 (1996).
    41. B.R. Hunt, K.M. Khanin, Y.G. Sinai, J.A. Yorke, Fractal properties of critical invariant curves, J. Stat. Phys., 85 (1-2), 261-276 (1996).
    42. A.A. Dzhalilov, K.M. Khanin, Ob invariantnoi mere dlya gomeomorfizmov okruzhnosti s odnoi tochkoi izloma, Uspekhi mat. nauk, 51:6(312), 201–202 (1996) [A.A. Dzhalilov, K.M. Khanin, On an invariant measure for homeomorphisms of the circle with a single break point, Russ. Math. Surv., 51(6), 1198-1199 (1996)].
    43. K. Khanin, Yu. Kifer, Thermodynamic Formalism for Random Transformations, Amer. Math. Soc. Transl. Ser. 2, Vol. 171, 107-140 (1996) [Sinai's Moscow Seminar on Dynamical System, Edited by: L.A. Bunimovich, B.M. Gurevich, Ya.B. Pesin. AMS, 1996, 247 pp. ISBN-10: 0-8218-0456-1, ISBN-13: 978-0-8218-0456-8].
    44. 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 (k shestidesyatiletiyu so dnya rozhdeniya), Uspekhi mat. nauk, 51:4(310), 179–191 (1996) [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 Grigorʹevich Sinaĭ (on the occasion of his sixtieth birthday), Russ. Math. Surv., 51(4), 765–778 (1996)].
    45. K. M. Khanin, D. L. Lebovits, A. E. Mazel’, Ya. G. Sinai, Sluchainye bluzhdaniya bez samoperesechenii v pyati i bolee izmereniyakh: podkhod s ispol’zovaniem polimernykh razlozhenii, Uspekhi mat. nauk, 50:2(302), 175-206 (1995) [K.M. Khanin, J.L. Lebowitz, A.E. Mazel, Ya.G. Sinai, Self-avoiding walks in five or more dimensions: Polymer expansion approach, Russ. Math. Surv., 50(2), 403-434 (1995)].
    46. K.M. Khanin, A.E. Mazel’, S.B. Shlosman, Ya.G. Sinai, Loop condensation effects in the behaviour of random walks, Prog. Probab. 34, 167-184 (1994) [Freidlin, Mark I. (ed.), The Dynkin Festschrift. Markov processes and their applications. In celebration of Eugene B. Dynkin's 70th birthday. Birkhäuser Boston, Inc., Boston, MA, 1994. xxxii+413 pp. ISBN: 0-8176-3696-X].
    47. A. Dzhalilov, K.M. Khanin, Spektral’nye svoistva otobrazheniya Feigenbauma, Uzbekskii matem. zhurnal, 1992.
    48. Ya. G. Sinai, K. M. Khanin, Peremeshivanie nekotorykh klassov spetsial’nykh potokov nad povorotom okruzhnosti, Funkts. analiz i ego pril., 26(3), 1-21 (1992) [Ya.G. Sinai, K.M. Khanin, Mixing for some classes of special flows over rotations of the circle: Mixing for some classes of special flows over rotations of the circle, Funct. Anal. Appl., 26(3), 155-169 (1992)].
    49. K.M. Khanin, Universal estimates for critical circle mappings, Chaos 1(2), 181-186 (1991).
    50. V.A. Gurvich, K.M. Khanin, Gauss distribution for sums of distances (in Russian), Dokl. Akad. nauk SSSR, 316 (2), 279-284 (1991) [V.A. Gurvich, K.M. Khanin, A Gaussian distribution for sums of distances, Sov. Math., Dokl. 43(1), 63-68 (1991)].
    51. V.A. Gurvich, K.M. Khanin, Poisson-distribution for the number of pairs of close points (in Russian), Dokl. Akad. nauk SSSR, 316 (3), 533-538 (1991) [V.A. Gurvich, K.M. Khanin, A Poisson distribution for the number of pairs of close points, Sov. Math., Dokl. 43(1), 122-127 (1991)].
    52. E.B. Vul, Ya.G. Sinaĭ, K.M. Khanin, Feigenbaum universality and the thermodynamic formalism, Advanced Series in Nonlinear Dynamics, 1, 501–540 (1991) [Dynamical systems. Collection of papers. Edited by Ya. G. Sinaĭ. World Scientific Publishing Co., Inc., Teaneck, NJ, 1991. x+673 pp. ISBN: 981-02-0436-1; 981-02-0437-X].
    53. K.M. Khanin, Ya.G. Sinaĭ, The renormalization group method and Kolmogorov-Arnolʹd-Moser theory, Advanced Series in Nonlinear Dynamics, 1, 541–566 (1991) [Dynamical systems. Collection of papers. Edited by Ya. G. Sinaĭ. World Scientific Publishing Co., Inc., Teaneck, NJ, 1991. x+673 pp. ISBN: 981-02-0436-1; 981-02-0437-X].
    54. Ya.G. Sinaĭ, K.M. Khanin, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Advanced Series in Nonlinear Dynamics, 1, 567–597 (1991) [Dynamical systems. Collection of papers. Edited by Ya. G. Sinaĭ. World Scientific Publishing Co., Inc., Teaneck, NJ, 1991. x+673 pp. ISBN: 981-02-0436-1; 981-02-0437-X].
    55. E.B. Vul, K.M. Khanin, Gomeomorfizmy okruzhnosti s osobennostyami tipa izloma, Uspekhi mat. nauk, 45:3(273), 189–190 (1990) [E.B. Vul, K.M. Khanin, Homeomorphisms of the circle with singularities of “break” type, Russ. Math. Surv., 45(3), 229–230 (1990)].
    56. K.M. Khanin, Thermodynamic formalism for critical circle mappings, In: Chaos/Khaos, 71-77, AIP, New York, 1990 [Chaos/Khaos: Soviet-American perspectives on nonlinear science. Papers from the Soviet-American Conference, Woods Hole, Massachusetts, July 1989. Ed. by D.K. Campbell. American Institute of Physics, New York, 1990. xvi+496 pp. ISBN: 0-88318-777-9; 0-88318-778-7].
    57. Ya. G. Sinai, K. M. Khanin, Gladkost’ sopryazhenii diffeomorfizmov okruzhnosti s povorotami, Uspekhi mat. nauk, 44:1(265), 57–82 (1989) [Ya.G. Sinai, K.M. Khanin, Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Russ. Math. Surv., 44(1), 69-99 (1989)].
    58. Ya.G. Sinai, K.M. Khanin, Renormalization group method in the theory of dynamical systems, Int. J. Mod. Phys. B 2 (2), 147-165 (1988).
    59. V. M. Kharlamov, A. N. Varchenko, V. M. Petkov, Ya. G. Sinai, K. M. Khanin, S. Yu. Dobrokhotov, A. B. Givental’, V. A. Dobrynin, Zasedaniya seminara imeni I.G. Petrovskogo po differentsial’nym uravneniyam i matematicheskim problemam fiziki, Uspekhi mat. nauk, 43:3(261), 239–245 (1988).
    60. K.M. Khanin, Ya.G. Sinai, A new proof of M. Herman's theorem, Commun. Math. Phys., 112 (1), 89-101 (1987).
    61. A.I. Gol’berg, V.A. Gurvich, M.Yu. Rozenblyum, K.M. Khanin, Usloviya razreshimosti po dominirovaniyu vognutykh igr $n$ lits, Uspekhi mat. nauk, 42:2(254), 223–224 (1987) [A.I. Gol’berg, V.A. Gurvich, M.Yu. Rozenblyum, K.M. Khanin, The conditions of solubility by domination of concave n-person games, Russ. Math. Surv., 42(2), 277-278 (1987)].
    62. Ya.G. Sinai, K.M. Khanin, L.N. Shchur, Novyi podkhod k postroeniyu nepodvizhnykh tochek renormgruppy v dinamicheskikh sistemakh, Izvestiya vysshikh uchebnykh zavedenii. Radiofizika, 29(9), 1061–1066 (1986) [Ya.G. Sinai, K.M. Khanin, L.N. Shchur, A new approach to the construction of fixed points of the renormalization group in dynamical systems, Radiophysics and Quantum Electronics, 29(9), 803-808 (1986)].
    63. J.B. Vul, Ja.G. Szinaj, K.M. Khanin, Feigenbaum-univerzalitás és a termodinamikai formalizmus, Alkalmazott Matematikai Lapok (Hungary), 11(1-2), 201-237 (1985) [E.B. Vul, Ya.G. Sinaj, K.M. Khanin, Feigenbaum universality and the thermodynamic formalism (in Hungarian)].
    64. I.M. Khalatnikov, E.M. Lifshitz, K.M. Khanin, L.N. Shchur, Ya.G. Sinai, On the stochasticity in relativistic cosmology, J. Stat. Phys., 38 (1-2), 97-114 (1985).
    65. E.B. Vul, Ya.G. Sinai, K.M. Khanin, Universal’nost’ Feigenbauma i termodinamicheskii formalizm, Uspekhi mat. nauk, 39:3(237), 3–37 (1984) [E.B. Vul, Ya.G. Sinai, K.M. Khanin, Feigenbaum universality and the thermodynamic formalism, Russ. Math. Surv., 39(3), 1-40 (1984)].
    66. I.M. Khalatnikov, E.M. Lifshitz, K.M. Khanin, L.N. Shchur, Ya.G. Sinai, On the stochastic properties of relativistic cosmological models near the singularity, In: General Relativity and Gravitation. Ed. by B. Bertotti, F. de Felice and A. Pascolini, 1984, pp. 343-349, Reidel, xvi+517 pp.
    67. I.M. Khalatnikov, E.M. Lifshitz, K.M. Khanin, L.N. Shchur, Ya.G. Sinai, On The Stochasticity In Relativistic Cosmology, Preprint IC/84/64, Jun 1984. 29pp.
    68. E.M. Lifshits, I.M. Khalatnikov, Ya.G. Sinai, K.M. Khanin, L.N. Shchur, O stokhasticheskikh svoistvakh relyativistskikh kosmologicheskikh modelei vblizi osoboi tochki, Pis’ma v ZhETF, 38 (2), 79-82 (1983) [E.M. Lifshitz, I.M. Khalatnikov, Ya.G. Sinai, K.M. Khanin, L.N. Shchur., On the stochastic properties of relativistic cosmological models near the singularity, JETP Lett., 38 (2), 91-94 (1983)].
    69. A. I. Gol’berg, Ya. G. Sinai, K. M. Khanin, Universal’nye svoistva dlya posledovatel’nostei bifurkatsii utroeniya perioda, Uspekhi mat. nauk, 38:1(229), 159–160 (1983) [A.I. Gol’berg, Ya.G. Sinai, K.M. Khanin, Universal properties for sequences of bifurcations of period three, Russ. Math. Surv., 38(1), 187-188 (1983)].
    70. V.V. Anshelevich, K.M. Khanin, Ya.G. Sinai, Symmetric random walks in random environments, Commun. Math. Phys., 85 (3), 449-470 (1982).
    71. K.M. Khanin, Quasi-periodic motions of vortex systems, Physica D 4 (2), 261-269 (1982).
    72. E.B. Vul, K.M. Khanin, O neustoichivoi separatrise nepodvizhnoi tochki Feigenbauma, Uspekhi mat. nauk, 37:5(227), 173–174 (1982) [E.B. Vul, K.M. Khanin, The unstable separatrix of Feigenbaum's fixed-point, Russ. Math. Surv., 37(5), 200–201 (1982)].
    73. K.M. Khanin, Sushchestvovanie uslovno-periodicheskikh dvizhenii dlya sistemy ploskikh vikhrei, Uspekhi mat. nauk, 36:1(217), 231-232 (1981) [K.M. Khanin, The existence of conditionally periodic motions for a system of plane vortices, Russ. Math. Surv., 36(1), 234-235 (1981)].
    74. K.M. Khanin, E.B. Vul, Circle homeomorphisms with weak discontinuities, Adv. Sov. Math., 3, 57-98 (1991) [Dynamical systems and statistical mechanics, Pap. Semin. Stat. Phys., Moscow/USSR. Ed. by Ya. G. Sinaĭ. AMS, 1991, 254 pp. ISBN: 0-8218-4102-5.].
    75. K.M. Khanin, Otsutstvie fazovykh perekhodov v odnomernykh dal’nodeistvuyushchikh spinovykh sistemakh so sluchainym gamil’tonianom, TMF, 43(2), 253–260 (1980) [K.M. Khanin, Absence of phase transitions in one-dimensional long-range spin systems with random Hamiltonian, Theor. Math. Phys., 43(2), 445-449 (1980)].
    76. K.M. Khanin, Ya.G. Sinai, Existence of free energy for models with long-range random Hamiltonians, J. Stat. Phys., 20 (6), 573-584 (1979).