The Abel Prize award to Ya. G. Sinai

A. I. Bufetov   ; B. M. Gurevich   ; K. M. Khanin   ; F. Cellarosi

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 5, pp. 931-956

Bibliographie

[1] V. V. Anshelevich, K. M. Khanin, Ya. G. Sinai, “Symmetric random walks in random environments”, Comm. Math. Phys., 85:3 (1982), 449–470 | DOI | MR | Zbl

[2] V. I. Arnol'd, “Small denominators. I. Mappings of the circumference onto itself”, Amer. Math. Soc. Transl. Ser. 2, 46, Amer. Math. Soc., Providence, RI, 1965, 213–284 | MR | Zbl

[3] V. I. Arnol'd, “Topological and ergodic properties of closed 1-forms with incommensurable periods”, Funct. Anal. Appl., 25:2 (1991), 81–90 | DOI | MR | Zbl

[4] M. Avdeeva, D. Li, Ya. G. Sinai, “New {E}rdős–{K}ac type theorems for signed measures on square-free integers”, J. Statist. Phys., 154:1-2 (2014), 327–333 | DOI | MR | Zbl

[5] M. Avdeeva, D. Li, Ya. G. Sinai, “New limiting distributions for the {M}öbius function”, Mosc. J. Comb. Number Theory, 4:1 (2014), 3–51

[6] Yu. Bakhtin, E. Cator, K. Khanin, “Space-time stationary solutions for the Burgers equation”, J. Amer. Math. Soc., 27:1 (2014), 193–238 | DOI | MR | Zbl

[7] P. M. Bleher, Ja. G. Sinai, “Investigation of the critical point in models of the type of Dyson's hierarchical models”, Comm. Math. Phys., 33:1 (1973), 23–42 | DOI | MR

[8] P. M. Bleher, Ya. G. Sinai, “Critical indices for Dyson's asymptotically-hierarchical models”, Comm. Math. Phys., 45:3 (1975), 247–278 | DOI | MR

[9] C. Boldrighini, A. Pellegrinotti, E. Presutti, Ya. G. Sinai, M. R. Soloveichik, “Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics”, Comm. Math. Phys., 101:3 (1985), 363–382 | DOI | MR

[10] J. Bourgain, Ya. G. Sinai, “Limit behaviour of large Frobenius numbers”, Russian Math. Surveys, 62:4 (2007), 713–725 | DOI | DOI | MR | Zbl

[11] A. Bufetov, Ya. G. Sinai, C. Ulcigrai, “A condition for continuous spectrum of an interval exchange transformation”, Representation theory, dynamical systems, and asymptotic combinatorics (St. Petersburg, June 8–13, 2004), Amer. Math. Soc. Transl. Ser. 2, 217, eds. V. Kaimanovich, A. Lodkin, Amer. Math. Soc., Providence, RI, 2006, 23–35 | MR | Zbl

[12] F. Cellarosi, Ya. G. Sinai, “The {M}öbius function and statistical mechanics”, Bull. Math. Sci., 1:2 (2011), 245–275 | DOI | MR | Zbl

[13] F. Cellarosi, Ya. G. Sinai, “Ergodic properties of square-free numbers”, J. Eur. Math. Soc. (JEMS), 15:4 (2013), 1343–1374 | DOI | MR | Zbl

[14] F. Cellarosi, Ya. G. Sinai, “Non-standard limit theorems in number theory”, Prokhorov and contemporary probability theory, Springer Proc. Math. Statist., 33, Springer, Heidelberg, 2013, 197–213 | DOI | MR | Zbl

[15] E. I. Dinaburg, Ya. G. Sinai, “The one-dimensional Schrödinger equation with a quasiperiodic potential”, Funct. Anal. Appl., 9:4 (1975), 279–289 | DOI | MR | Zbl

[16] E. I. Dinaburg, Ya. G. Sinai, “Statistics of solutions of the integral equation $ax-by=\pm 1$”, Funct. Anal. Appl., 24:3 (1990), 165–171 | DOI | MR | Zbl

[17] R. Dobrushin, R. Kotecký, S. Shlosman, Wulff construction. A global shape from local interaction, Transl. Math. Monogr., 104, Amer. Math. Soc., Providence, RI, 1992, x+204 pp. | MR | Zbl

[18] W. E, K. Khanin, A. Mazel, Y. Sinai, “Probability distribution functions for the random forced Burgers equation”, Phys. Rev. Lett., 78:10 (1997), 1904–1907 | DOI

[19] W. E, K. Khanin, A. Mazel, Ya. Sinai, “Invariant measures for Burgers equation with stochastic forcing”, Ann. of Math. (2), 151:3 (2000), 877–960 | DOI | MR | Zbl

[20] W. E, J. C. Mattingly, Ya. Sinai, “Gibbsian dynamics and ergodicity for the stochastically forced Navier–Stokes equation”, Comm. Math. Phys., 224:1 (2001), 83–106 | DOI | MR | Zbl

[21] J. Fröhlich, T. Spencer, P. Wittwer, “Localization for a class of one-dimensional quasi-periodic Schrödinger operators”, Comm. Math. Phys., 132:1 (1990), 5–25 | DOI | MR | Zbl

[22] A. I. Gol'berg, Ya. G. Sinai, K. M. Khanin, “Universal properties for sequences of bifurcations of period three”, Russian Math. Surveys, 38:1 (1983), 187–188 | DOI | MR | Zbl

[23] Sh. Goldstein, J. L. Lebowitz, M. Aizenman, “Ergodic properties of infinite systems”, Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, WA, 1974), Lecture Notes in Phys., 38, Springer, Berlin, 1975, 112–143 | DOI | MR | Zbl

[24] A. O. Golosov, “Localization of random walks in one-dimensional random environments”, Comm. Math. Phys., 92:4 (1984), 491–506 | DOI | MR | Zbl

[25] A. Granville, “Smooth numbers: computational number theory and beyond”, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., 44, Cambridge Univ. Press, Cambridge, 2008, 267–323 | MR | Zbl

[26] B. M. Gurevich, Ya. G. Sinai, Yu. M. Sukhov, “On invariant measures of dynamical systems of one-dimensional statistical mechanics”, Russian Math. Surveys, 28:5 (1973), 49–86 | DOI | MR | Zbl

[27] M. R. Herman, “Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations”, Inst. Hautes Études Sci. Publ. Math., 49:1 (1979), 5–233 | DOI | MR | Zbl

[28] H. Holden, R. Piene (eds.), The Abel prize 2003–2007. The first five years, Springer-Verlag, Berlin, 2010, xii+326 pp. | DOI | MR | Zbl

[29] H. Holden, R. Piene (eds.), The Abel prize 2008–2012, Springer, Heidelberg, 2014, xviii+571 pp. | DOI | MR | Zbl

[30] Y. Katznelson, D. Ornstein, “The differentiability of the conjugation of certain diffeomorphisms of the circle”, Ergodic Theory Dynam. Systems, 9:4 (1989), 643–680 | DOI | MR | Zbl

[31] H. Kesten, M. V. Kozlov, F. Spitzer, “A limit law for random walk in a random environment”, Compos. Math., 30:2 (1975), 145–168 | MR | Zbl

[32] K. M. Khanin, Ya. G. Sinai, “Renormalization group method and the KAM theory”, Nonlinear phenomena in plasma physics and hydrodynamics, ed. R. Z. Sagdeev, Mir, M., 1986, 31–64

[33] K. M. Khanin, Ya. G. Sinai, “A new proof of M. Herman's theorem”, Comm. Math. Phys., 112:1 (1987), 89–101 | DOI | MR | Zbl

[34] K. Khanin, A. Teplinsky, “Herman's theory revisited”, Invent. Math., 178:2 (2009), 333–344 | DOI | MR | Zbl

[35] A. V. Kochergin, “Nondegenerate saddle points and the absence of mixing in flows on surfaces”, Proc. Steklov Inst. Math., 256 (2007), 238–252 | DOI | MR | Zbl

[36] A. N. Kolmogorov, “Novyi metricheskii invariant tranzitivnykh dinamicheskikh sistem i avtomorfizmov prostranstv Lebega”, Dokl. AN SSSR, 119:5 (1958), 861–864 | MR | Zbl

[37] A. N. Kolmogorov, “Ob entropii na edinitsu vremeni kak metricheskom invariante avtomorfizmov”, Dokl. AN SSSR, 124:4 (1959), 754–755 | MR | Zbl

[38] J. Kułaga-Przymus, M. Lemańczyk, B. Weiss, On invariant measures for $\mathscr{B}$-free systems, 2014, 45 pp., arXiv: 1406.3745

[39] O. E. Lanford, III, “The classical mechanics of one-dimensional systems of infinitely many particles. I. An existence theorem”, Comm. Math. Phys., 9:3 (1968), 176–191 | DOI | MR | Zbl

[40] D. Li, Ya. G. Sinai, “Blow ups of complex solutions of the 3D Navier–Stokes system and renormalization group method”, J. Eur. Math. Soc. (JEMS), 10:2 (2008), 267–313 | DOI | MR | Zbl

[41] J. Marklof, “The asymptotic distribution of {F}robenius numbers”, Invent. Math., 181:1 (2010), 179–207 | DOI | MR | Zbl

[42] J. C. Mattingly, Ya. G. Sinai, “An elementary proof of the existence and uniqueness theorem for the Navier–Stokes equations”, Commun. Contemp. Math., 1:4 (1999), 497–516 | DOI | MR | Zbl

[43] L. D. Meshalkin, Ia. G. Sinai, “Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid”, J. Appl. Math. Mech., 25:6 (1961), 1700–1705 | DOI | MR | Zbl

[44] R. A. Minlos, Ya. G. Sinai, “The phenomenon of ‘phase separation’ at low temperatures in some lattice models of a gas. I”, Math. USSR-Sb., 2:3 (1967), 335–395 | DOI | MR

[45] R. A. Minlos, Ya. G. Sinai, “Yavlenie ‘razdeleniya faz’ pri nizkikh temperaturakh v nekotorykh reshetchatykh modelyakh gaza. II”, Tr. MMO, 19, Izd-vo Mosk. un-ta, M., 1968, 113–178 | MR

[46] 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 | DOI | DOI | MR | Zbl

[47] R. Peckner, “Uniqueness of the measure of maximal entropy for the squarefree flow”, Israel J. Math. (to appear); 2012 (v8 – 2014), 18 pp., arXiv: 1205.2905

[48] Ya. B. Pesin, “General theory of smooth dynamical systems”, Dynamical systems. II. Ergodic theory with applications to dynamical systems and statistical mechanics, Encyclopaedia Math. Sci., 2, Springer-Verlag, Berlin, 1989, 99–206 | MR | MR | Zbl

[49] S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems”, Theoret. Math. Phys., 25:3 (1975), 1185–1192 | DOI | MR

[50] S. A. Pirogov, Ya. G. Sinai, “Phase diagrams of classical lattice systems. (Continuation)”, Theoret. Math. Phys., 26:1 (1976), 39–49 | DOI | MR

[51] A. M. Polyakov, “Turbulence without pressure”, Phys. Rev. E (3), 52:6 (1995), 6183–6188 | DOI | MR

[52] V. A. Rokhlin, Ya. G. Sinai, “Construction and properties of invariant measurable partitions”, Soviet Math. Dokl., 2 (1961), 1611–1614 | MR | Zbl

[53] V. Shchur, Ya. Sinai, A. Ustinov, “Limiting distribution of {F}robenius numbers for $n=3$”, J. Number Theory, 129:11 (2009), 2778–2789 | DOI | MR | Zbl

[54] Ya. G. Sinai, “O ponyatii entropii dinamicheskoi sistemy”, Dokl. AN SSSR, 124:4 (1959), 768–771 | MR | Zbl

[55] Ja. G. Sinai, “Geodesic flows on manifolds of negative constant curvature”, Soviet Math. Dokl., 1 (1960), 335–339 | MR | Zbl

[56] Ja. G. Sinai, “The central limit theorem for geodesic flows on manifolds of constant negative curvature”, Soviet Math. Dokl., 1 (1960), 983–987 | MR | Zbl

[57] Ya. G. Sinai, “Dynamical systems with countably-multiple Lebesgue spectrum. I”, Amer. Math. Soc. Transl. Ser. 2, 39, Amer. Math. Soc., Providence, RI, 1964, 83–110 | MR | Zbl

[58] Ja. G. Sinai, “Geodesic flows on compact surfaces of negative curvature”, Soviet Math. Dokl., 2 (1961), 106–109 | MR | Zbl

[59] Ja. G. Sinai, “Weak isomorphism of transformations with an invariant measure”, Soviet Math. Dokl., 3 (1963), 1725–1729 | MR | Zbl

[60] Ya. G. Sinai, “O slabom izomorfizme preobrazovanii s invariantnoi meroi”, Matem. sb., 63(105):1 (1964), 23–42 | MR

[61] Ya. G. Sinai, “Classical dynamical systems with countably-multiple Lebesgue spectrum. II”, Amer. Math. Soc. Transl. Ser. 2, 68, Amer. Math. Soc., Providence, RI, 1968, 34–38 | MR | Zbl

[62] Ya. G. Sinai, “Markov partitions and $C$-diffeomorphisms”, Funct. Anal. Appl., 2:1 (1968), 61–82 | DOI | MR | Zbl

[63] Ya. G. Sinai, “Construction of Markov partitions”, Funct. Anal. Appl., 2:3 (1968), 245–253 | DOI | MR | Zbl

[64] Ya. G. Sinai, “Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards”, Russian Math. Surveys, 25:2 (1970), 137–189 | DOI | MR | Zbl

[65] Ya. G. Sinai, “Gibbs measures in ergodic theory”, Russian Math. Surveys, 27:4 (1972), 21–69 | DOI | MR | Zbl

[66] Ya. G. Sinai, “Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom”, Funct. Anal. Appl., 6:1 (1972), 35–43 | DOI | MR | Zbl

[67] Ya. G. Sinai, “Construction of dynamics in one-dimensional systems of statistical mechanics”, Theoret. Math. Phys., 11:2 (1972), 487–494 | DOI | MR

[68] Ja. G. Sinai, “Construction of a cluster dynamic for the dynamical systems of statistical mechanics”, Moscow Univ. Math. Bull., 29:1 (1974), 124–129 | MR

[69] Ya. G. Sinai, “Stokhastichnost dinamicheskikh sistem”, Nelineinye volny, Nauka, M., 1979, 192–212

[70] Ya. G. Sinai, “Ergodic properties of the Lorentz gas”, Funct. Anal. Appl., 13:3 (1979), 192–202 | DOI | MR | Zbl

[71] Ya. G. Sinai, “The limiting behavior of a one-dimensional random walk in a random medium”, Theory Probab. Appl., 27:2 (1983), 256–268 | DOI | MR | Zbl

[72] Ya. G. Sinai, “Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential”, J. Statist. Phys., 46:5-6 (1987), 861–909 | DOI | MR | Zbl

[73] Ya. G. Sinai, “Statistics of shocks in solutions of inviscid Burgers equation”, Comm. Math. Phys., 148:3 (1992), 601–621 | DOI | MR | Zbl

[74] Ya. G. Sinai, K. M. Khanin, “Smoothness of conjugacies of diffeomorphisms of the circle with rotations”, Russian Math. Surveys, 44:1 (1989), 69–99 | DOI | MR | Zbl

[75] 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 | DOI | MR | Zbl

[76] Ya. G. Sinai, M. R. Soloveichik, “One-dimensional classical massive particle in the ideal gas”, Comm. Math. Phys., 104:3 (1986), 423–443 | DOI | MR | Zbl

[77] Ya. G. Sinai, C. Ulcigrai, “Weak mixing in interval exchange transformations of periodic type”, Lett. Math. Phys., 74:2 (2005), 111–133 | DOI | MR | Zbl

[78] Ya. G. Sinai, C. Ulcigrai, “A limit theorem for Birkhoff sums of non-integrable functions over rotations”, Geometric and probabilistic structures in dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317–340 | DOI | MR | Zbl

[79] Ya. G. Sinai, C. Ulcigrai, “Renewal-type limit theorem for the Gauss map and continued fractions”, Ergodic Theory Dynam. Systems, 28:2 (2008), 643–655 | DOI | MR | Zbl

[80] A. V. Ustinov, “On the statistical properties of elements of continued fractions”, Dokl. Math., 79:1 (2009), 87–89 | DOI | MR | Zbl

[81] A. V. Ustinov, “On the distribution of {F}robenius numbers with three arguments”, Izv. Math., 74:5 (2010), 1023–1049 | DOI | DOI | MR | Zbl

[82] K. L. Volkovysskii, Ya. G. Sinai, “Ergodic properties of an ideal gas with an infinite number of degrees of freedom”, Funct. Anal. Appl., 5:3 (1971), 185–187 | DOI | MR | Zbl

[83] E. B. Vul, Ya. G. Sinai, K. M. Khanin, “Feigenbaum universality and the thermodynamic formalism”, Russian Math. Surveys, 39:3 (1984), 1–40 | DOI | MR | Zbl