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YA. G. SINAI Bibliography 1. On the distribution of the first positive sum for the sequence of independent random variables, Teor. Veroyatnost. i Primenen., 2 (1957), ; translated in Theory Probab.

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YA. G. SINAI Bibliography 1. On the distribution of the first positive sum for the sequence of independent random variables, Teor. Veroyatnost. i Primenen., 2 (1957), ; translated in Theory Probab. Appl., 2 (1957), no. 1, On the notion of entropy for a dynamic system (Russian), Dokl. Akad. Nauk SSSR, 124 (1959), no. 4, Flows with finite entropy (Russian), Dokl. Akad. Nauk SSSR, 125 (1959), no. 6, Geodesic flows on manifolds of negative constant curvature, Dokl. Akac. Nauk SSSR, 131 (1960), no. 4, ; translated in Soviet Math. Dokl., 1 (1960), no. 2, The central limit theorem for geodesic flows on manifolds of constant negative curvature, Dokl. Akad. Nauk SSSR, 133 (1960), no. 6, ; translated in Soviet Math. Dokl., 1 (1960), no. 4, Dynamical systems and stationary Markov processes, Teor. Veroyatnost. i Primenen., 5 (1960), ; translated in Theory Probab. Appl., 5 (1960), no. 3, (with L. D. Meshalkin), Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid, Prikl. Mat. Meh., 25 (1961), ; translated in J. Appl. Math. Mech., 25 (1961), Geodesic flows on compact surfaces of negative curvature, Dokl. Akad. Nauk SSSR, 136 (1961), no. 3, ; translated in Soviet Math. Dokl., 2 (1961), no. 1, Dynamical systems with countable Lebesque spectrum. I., Izv. Akad. Nauk SSSR Ser. Mat., 25 (1961), ; translated in Amer. Math. Soc. transl. (2), 39 (1964), (with V. A Rokhlin), The structure and properties of invariant measurable partitions, Dokl. Akad. Nauk SSSR, 141 (1961), no. 5, ; translated in Soviet Math. Dokl., 2 (1961), no. 4 6, YA. G. SINAI - Bibliography (with V. I. Arnold), Small perturbations of the automorphisms of the torus, Dokl. Akad. Nauk SSSR, 144 (1962), no. 4, ; translated in Soviet Math. Dokl., 3 (1962), no. 3, A weak isomorphism of transformations with invariant measure, Dokl. Akad. Nauk SSSR, 147 (1962), no. 4, ; translated in Soviet Math. Dokl., 3 (1962), no. 6, On limit theorems for stationary processes, Teor. Veroyatnost. i Primenen., 7 (1962), ; translated in Theory Probab. Appl., 7 (1962), no. 2, Probabilistic ideas in ergodic theory, Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm. Translated in Amer. Math. Soc. transl. (2), 31 (1963), On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics, Dokl. Akad. Nauk SSSR, 153 (1963), no. 6, ; translated in Soviet Math. Dokl., 4 (1963), no. 6, Some remarks on the spectral properties of ergodic dynamical systems, Uspehi Mat. Nauk, 18 (1963), no. 5(113), 41 54; translated in Russian Math. Surveys, 18 (1963), no. 5, On a physical system with positive entropy (Russian), Vestnik Moskov. Univ. Ser. I Mat. Meh., 1963 (1963), no. 5, On higher order spectral measures of ergodic stationary processes, Teor. Veroyatnost. i Primenen., 8 (1964), ; translated in Theory Probab. Appl., 8 (1964), no. 4, On a weak isomorphism of transformations with invariant measure, Mat. Sb. (N.S.), 63 (105) (1964), 23 42; translated in Amer. Math. Soc. trasl. (2), 57 (1966), Classical dynamical systems with countably-multiple Lebesque spectrum. II., Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), 15 68; translated in Amer. Math. Soc. transl. (2), 68 (1968), The asymptotic behavior of the number of closed geodesics on a compact manifold of negative curvature, Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), ; translated in Amer. Math. Soc. transl. (2), 73 (1968), YA. G. SINAI - Bibliography (with R. A.Minlos), The phenomenon of separation of phases at low temperatures in certain lattice models of a gas. I., Mat. Sb. (N.S.), 73 (115) (1967), ; translated in Math. USSR-Sb., 2 (1967), no. 3, A lemma from measure theory, Mat. Zametki, 2 (1967), ; translated in Math. Notes, 2 (1967), no. 4, (with D. V. Anosov), Certain smooth ergodic systems, Uspehi Mat. Nauk, 22 (1967), no. 5, ; translated in Russian Math. Surveys, 22 (1967), no. 5, Markov Partitions and U-diffeomorphisms, Funkcional. Anal. i Priložen., 2 (1968), no. 1, 64 89; translated in Funct. Anal. Appl., 2 (1968), no. 1, Construction of Markov Partitions, Funkcional. Anal. i Priložen., 2 (1968), no. 3, 70 80; translated in Funct. Anal. Appl., 2 (1968), no. 3, (with R. A. Minlos), The phenomenon of separation of phases at low temperatures, II, Trudy Moscov. Mat. Obš c., 19 (1968), ; translated in Trans. Moscow Math. Soc., 19 (1968), Theory of dynamical systems. Part I: Ergodic theory., Lectures held in Warsaw, Spring, English edition by A. Szankowski, based on notes in Polish prepared by J. Strelcyn and issued by the University of Warsaw, Lecture Notes Series, No. 23 Matematisk Institut, Aarhus Universitet, Aarhus 1970 a-c+viii+122 pp. 29. Dynamical systems with elastic reflections, Uspehi Mat. Nauk, 25 (1970), no. 2(152), ; translated in Russian Math. Surveys, 25 (1970), no. 2, (with R. A. Minlos), Spectra of stochastic arising operators in lattice models of a gas, Teoret. Mat. Fiz., 2 (1970), ; translated in Theoret. Math. Phys., 2 (1970), no. 2, Measures Invariantes des Y-systems, Actes du Congrs International des Mathmaticiens, (Nice, 1970), 2, Gauthier-Villars, Paris, (with K. Volkovysski), Ergodic properties of an ideal gas with an infinite number of degrees of freedom, Funkcional. Anal. i Priložen., 5 (1971), no. 3, 19 21; translated in Funct. Anal. Appl., 5 (1971), no. 3, (with A. N. Livšic), Invariant measures that are compatible with smoothness for transitive U-systems, Dokl. Akad. Nauk SSSR, 207 (1972), no. 5, ; translated in Soviet Math. Dokl., 13 (1972), no. 6, YA. G. SINAI - Bibliography Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom, Funkcional. Anal. i Priložen., 6 (1972), no. 1, 41 50, translated in Funct. Anal. Appl., 6 (1972), no. 1, (with A. Ya. Khelemski), A description of differentiations in algebras of local observables, Funkcional. Anal. i Priložen., 6 (1972), ; translated in Funct. Anal. Appl., 6 (1972), no. 4, Construction of the dynamics for one-dimensional systems of statistical mechanics, Teoret. Mat. Fiz., 11 (1972), no. 2, , translated in Theoret. Math. Phys., 11 (1972), no. 2, Gibbs measures in ergodic theory, Uspehi Mat. Nauk, 27 (1972), no. 4(166), 21 64; translated in Russian Math. Surveys, 27 (1972), no. 4, (with L. A. Bunimovich), On a fundamental theorem in the theory of dispersing billiards, Mat. Sb. (N.S.), 90(132) (1973), ; translated in Math. USSR-Sb., 19 (1973), no. 3, (with B. M. Gurevich and Yu. M. Sukhov), Invariant measures of dynamical systems of one-dimensional statistical mechanics, Uspehi Mat. Nauk, 28 (1973), no. 5(173), 45 82; translated in Russian Math. Surveys, 28 (1973), (with S. A. Pirogov), Phase transitions of the first kind for small perturbations of the Ising Model, Funkcional. Anal. i Priložen., 8 (1974), no. 1, 25 30; translated in Funct. Anal. Appl., 8 (1974), no. 1, (with Yu. M. Sukhov), On an existence theorem for the solutions of Bogoljubovs chain of equations, Teoret. Mat. Fiz., 19 (1974), ; translated in Theoret. Math. Phys., 19 (1974), no. 3, Construction of a cluster dynamics for dynamical systems of statistical mechanics, Vestnik Moskov. Univ. Ser. I Mat. Meh., 29 (1974), no. 1, ; translated in Moscow Univ. Math. Bull., 29 (1974), no. 1, (with P. M. Blekher), Critical indices for Dysons asymptotically-hierarchal models, Comm. Math. Phys., 45 (1975), no. 3, (with E. I. Dinaburg), The one-dimensional Schrdinger operator with quasi-periodic potential, Funkcional. Anal. i Priložen., 9 (1975), no. 4, 8 21; translated in Funct. Anal. Appl., 9 (1975), no. 4, YA. G. SINAI - Bibliography (with S. A. Pirogov), Phase diagrams of classical lattice systems, Teoret. Mat. Fiz., 25 (1975), no. 3, ; translated in Theoret. Math. Phys., 25 (1975), no. 3, Introduction to Ergodic Theory, Princeton University Press, Princeton, New Jersey USA, 1976, 144 pages. 47. Self-similar probability distribution, Teor. Veroyatnost i Primenen., 21 (1976), no. 1, 63 80; translated in Theory Probab. Appl., 21 (1976), no. 1, (with S. A. Pirogov), Phase diagrams of classical lattice systems (continuation), Teoret. Mat. Fiz., 26 (1976), no. 1, 61 76; translated in Theoret. Math. Phys., 26 (1976), no. 1, (with V. V. Anshelevich), Some questions on noncommutative ergodic theory, Uspehi Mat. Nauk, 31 (1976), no. 4(190), ; translated in Russian Math. Surveys, 31 (1976), no. 4, (with S. A. Pirogov), Ground states in the two-dimensional boson quantum fieldtheory, Ann. Physics, 109 (1977), no. 2, Billiard trajectories in a polyhedral angle, Uspehi Mat. Nauk, 33 (1978), no. 1 (199), ; translated in Russian Math. Surveys, 33 (1978), no. 1, Ergodic properties of a Lorentz gas, Funktsional. Anal. i Prilozhen., 13 (1979), no. 3, 46 59; translated in Funct. Anal. Appl., 13 (1979), no. 3, (with K. M. Khanin), Existence of free energy for models with long-range random Hamiltonians, J. Statist. Phys., 20 (1979), no. 6, Ergodic and kinetic properties of the Lorentz gas. Nonlinear dynamics, Annals of the New York Academy of Sciences, 357, New York Academy of Sciences, New York, (with E. B. Vul) Discovery of closed orbits of dynamical systems with the use of computers, J. Statist. Phys., 23 (1980), no. 1, (with E. B. Vul) A structurally stable mechanism of appearance of invariant hyperbolic sets, Multicomponent random systems, pp , Adv. Probab. Related Topics, 6, Dekker, New York, Theory of Phase Transitions. Rigorous results (Russian), Nauka, Moscow, 1980, pp. 208. YA. G. SINAI - Bibliography (with I. P. Cornfeld and S. V. Fomin) Ergodic Theory (Russian), Nauka, Moscow, 1980, pp (with L. A. Bunimovich), Markov partitions for dispersed billiards, Comm. Math. Phys., 78 (1980/81), no. 2, (with L. A. Bunimovich), Statistical properties of Lorentz gas with a periodic configuration of scatterers, Comm. Math. Phys., 78 (1980/81), no. 4, (with Ya. B. Pesin), Hyperbolicity and stochasticity of dynamical systems, Math. Phys. Rev. 2, , Soviet Sci. Rev. Sect. C: Math. Phys. Rev., 2, Harwood Academic, Chur, (with E. B. Vul), Hyperbolicity conditions for the Lorenz model. Nonlinear and turbulent processes in physics (Proc. Internat. Workshop, Kiev, 1979). Phys. D, 2 (1981), no. 1, The stochasticity of dynamical systems, Selecta Math. Soviet, 1 (1981), no. 1, Theory of Phase Transitions. Rigorous Results. N. Holland, (with I. P. Cornfeld and S. V. Fomin), Ergodic Theory, Springer-Verlag, Lorentz Gas and Random Walks, Mathematical problems in theoretical physics, Lecture Notes in Physics, 153, 12 14, Springer-Verlag, Berlin-New York, (with V. V. Anshelevich and K. M. Khanin), Symmetric random walks in random environments, Comm. Math. Phys., 85 (1982), no. 3, Commensurate-incommensurate phase transition in one-dimensional chains, J. Statist. Phys., 29 (1982), no. 3, The limiting behavior of a one-dimensional random walk in random medium, Teor. Veroyatnost. i Primenen., 27 (1982), no. 2, ; translated in Theory Probab., 27 (1982), no. 2, (with N. I. Chernov), Entropy of a gas of hard spheres with respect to the group of space-time shifts, Trudy Sem. Petrovsk., (1982), no. 8, ; translated in J. Math. Sci., 32 (1986), no. 4, (with Ya. B. Pesin), Gibbs measures for partially hyperbolic attractors, Ergodic Theory and Dynam. Systems, 2 (1982), no. 3 4, YA. G. SINAI - Bibliography (with A. Goldberg and K. M. Khanin), Universal properties of sequences of periodtripling bifurcations, Uspehi Mat. Nauk, 38 (1983), no. 1(229), ; translated in Russian Math. Surveys, 38 (1983), no. 1, (with C. Boldrighini, and L. A. Bunimovich), On the Boltzmann equation for the Lorentz gas, J. Statist. Phys., 32 (1983), no. 3, Ground states of the Dyson antiferromagnetic model, Teoret. Mat. Fiz., 57 (1983), no. 1, ; translated in Theoret. Math. Phys., 57 (1983), no. 1, (with S. Burkov), Phase diagrams of the one-dimensional lattice models with longrange antiferromagnetic interaction, Uspekhi Mat. Nauk, 38 (1983), no. 4(232), ; translated in Russian Math. Surveys, 38 (1983), no. 4, (with S. Burkov), Rotation numbers that have nothing to do with KAM theory, Funktsional. Anal. i Prilozhen., 18 (1984), no. 4, 73 74; translated in Funct. Anal. Appl., 18 (1984), no. 4, (with N. Khimchenko), On the description of classical reflectionless potentials, Rep. Math. Phys., 20 (1984), no. 1, (with E. B. Vul and K. M. Khanin), Feigenbaum universality and thermodynamic formalism, Uspekhi Mat. Nauk, 39 (1984), no. 3, 3 37; translated in Russian Math. Surveys, 39 (1984), no. 3, (with K. M. Efimov), Hydrodynamic modes for a Lorentz gas with a periodic configuration of scatters (Russian), Some Problems in Modern Analysis, , Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, (with E. I. Dinaburg), An analysis of ANNNI model by Peierls contour method, Comm. Math. Phys., 98 (1985), no. 1, (with I. M. Khalatnikov, E. M. Lifshitz, K. M. Khanin, and L. N. Shchur) On the stochasticity in relativistic cosmology, J. Statist. Phys., 38 (1985), no. 1 2, An answer to a question by J. Milnor, Comment. Math. Helv., 60 (1985), no. 2, Lectures in Probability Theory. Part 1 (Russian), Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1985, pp Lectures in Probability Theory. Part 2 (Russian), Moskov. Gos. Univ. Mekh.-Mat. Fak., Moscow, 1986, pp. 106. YA. G. SINAI - Bibliography (with E. Presutti and M. Soloveichik), Hyperbolity and Mller-morphism for a model of classical statistical mechanics, Statistical physics and dynamical systems (Kszeg, 1984), , Progr. Phys., 10, Birkhuser Boston, Boston, MA, (with C. Boldrighini, A. Pellegrinotti, E. Presutti, and M. Soloveichik), Ergodic properties of semi-infinite one-dimensional system of statistical mechanics, Comm. Math. Phys., 101 (1985), no. 3, Structure of the spectrum of the Schrdinger operator with almost-periodic potential in the vicinity of its left edge, Funktsional. Anal. i Prilozhen., 19 (1985), no. 1, 42 48, 96; translated in Funct. Anal. Appl., 19 (1985), no. 1, (with L. A. Bunimovich), Erratum: Markov partition for dispersed billiards [Comm. Math. Phys., 78 (1980/81), no. 2, ]. Comm. Math. Phys., 107 (1986), no. 2, (with K. M. Khanin and L. N. Shchur), A new approach to the construction of fixed points of the renormalization group in dynamical systems, Izv. Vyssh. Uchebn. Zaved. Radiofiz., 29 (1986), no. 9, ; translated in Radiophys. and Quantum Electronics 29 (1986), no. 9, (with M. Soloveichik), One-dimensional classical massive particle in the ideal gas, Comm. Math. Phys., 104 (1986), no. 3, (with E. I. Dinaburg and A. E. Mazel), The ANNNI model and contour models with interaction, Mathematical Physics Reviews, 6, , Soviet Sci. Rev. Sect. C Math. Phys. Rev., 6, Harwood Academic Publ., Chur, (with K. Khanin), A new proof of Herman theorem, Comm. Math. Phys., 112 (1987), no. 1, Anderson localization for one-dimensional difference Schrödinger operator with quasi-periodic potential, J. Statist. Phys., 46 (1987), no. 5, (with N. I. Chernov), Ergodic properties of some systems of two-dimensional disks and three-dimensional balls, Uspekhi Mat. Nauk, 42 (1987), no. 3, ; translated in Russian Math. Surveys, 42 (1987), no. 3, (with K. M. Khanin), The renormalization group method in the theory of dynamical systems, Conference Renormalization Group 86 (Dubna, 1986), , , 407, Joint Inst. Nuclear Res., Dubna, (with E. I. Dinaburg), Contour models with interaction and their applications, Selecta Math. Soviet, 7 (1988), no. 3, YA. G. SINAI - Bibliography (with Ya. B. Pesin), On stable manifolds for a class of two-dimensional diffeomorphisms, Topology and Geometry-Rohlin Seminar, Lecture Notes in Math., Springer-Verlag, 1346 (1988), About A. N. Kolmogorovs work on the entropy of dynamical systems, Ergodic Theory Dynam. Systems, 8 (1988), no. 4, The absence of the Poisson distribution for spacings between quasi-energies in the quantum kicked-rotator model, Progress in chaotic dynamics. Phys. D, 33 (1988), no. 1 3, (with K. M. Khanin), Renormalization group method in the theory of dynamical systems, Internat. J. Modern Phys. B, 2 (1988), no. 2, (with L. Bunimovich), Spacetime chaos of coupled map lattices, Nonlinearity, 1 (1988), no. 4, (with Ya. Pesin), Space-time chaos in the system of weakly interactive hyperbolic systems, J. Geom. Phys., 5 (1988), no. 3, (with V. A. Chulaevski), Anderson localization for the 1D-discrete Schrödinger operator with two-frequency potential, Comm. Math. Phys., 125 (1989), no. 1, Limit theorems for multiple trigonometric Weyl sums, Trudy Mat. Inst. Steklov., 191 (1989), ; translated in Proc. Steklov Inst. Math., (1992), no. 2, Statistical mechanics and the theory of dynamical systems (with K. M. Khanin), Smoothness of conjugacies of diffeomorphisms of the circle with rotations, Uspekhi Mat. Nauk, 44 (1989), no. 1, 57 82, 247; translated in Russian Math. Surveys, 44 (1989), no. 1, Kolmogorovs works on ergodic theory, Ann. Probab., 17 (1989), no. 3, Hyperbolic billiards. A plenary address presented at the International Congress of Mathematicians held in Kyoto, August ICM-90. Mathematical Society of Japan, Tokyo; distributed outside Asia by the American Mathematical Society, Providence, RI, Mathematical problems in the theory of quantum chaos, Chaos (Woods Hole, MA, 1989), , Amer. Inst. Phys., New York, (with C. Series), Ising models on the Lobachevsky plane, Comm. Math. Phys., 128 (1990), no. 1, YA. G. SINAI - Bibliography (with L. Bunimovich and N. Chernov), Markov partitions for the two-dimensional hyperbolic billiards, Uspekhi Mat. Nauk, 45 (1990), no. 3(273), , 221; translated in Russian Math. Surveys, 45 (1990), no. 3, (with S. K. Nechaev), Scaling behavior of random walks with topological constraints, New trends in probability and statistics, 1 (Bakuriani, 1990), , VSP, Utrecht, Erratum: Some mathematical problems in the theory of quantum chaos, [Phys. A 163 (1990), no. 1, ]. Phys. A, 173 (1991), no. 1 2, Mathematical problems in the theory of quantum chaos, Geometric aspects of functional analysis ( ), 41 59, Lecture Notes in Math., 1469, Springer, Berlin, Hyperbolic billiards, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), , Math. Soc. Japan, Tokyo, (with E. I. Dinaburg) The statistics of the solutions of the integer equation ax by = 1, Funktsional. Anal. i Prilozhen. 24 (1990), no. 3, 1 8, 96; translated in Funct. Anal. Appl. 24 (1990), no. 3, Two results concerning asymptotic behavior of solutions of the Burgers equations with force, J. Statist. Phys., 64 (1991), no. 1-2, (with L. Bunimovich and N. I. Chernov), Statistical properties of two-dimensional hyperbolic billiards, Uspekhi Mat. Nauk, 46 (1991), no. 4(280), 43 92, 192; translated in Russian Math. Surveys, 46 (1991), no. 4, Finite-dimensional randomness, Uspekhi Mat. Nauk, 46 (1991), no. 3(279), ; translated in Russian Math. Surveys, 46 (1991), no. 3, Poisson distribution in a geometric problem, Dynamical systems and statistical mechanics (Moscow, 1991), , Adv. Soviet Math., 3, Amer. Math. Soc., Providence, RI, (with Ya. B. Pesin), Space-time chaos in chains of weakly interacting hyperbolic maps, Dynamical systems and statistical mechanics (Moscow, 1991), , Adv. Soviet Math., 3, Amer. Math. Soc., Providence, RI, (with V. A. Chulaevski), The exponential localization and structure of the spectrum for 1D quasi-periodic discrete Schrödinger operator, Rev. in Math. Phys., 3 (1991), no. 3, YA. G. SINAI - Bibliography Probability theory. An introductory course. Translated from the Russian and with a preface by D. Haughton. Springer Textbook. Springer-Verlag, Berlin, vi+138 pp (with A. E. Mazel), A limiting distribution connected with fractional parts of linear forms, Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), , Cambridge Univ. Press, Cambridge, Statistics of shocks in solutions of the Inviscid Burgers equation, Comm. Math. Phys., 148 (1992), no. 3, Distribution of some functionals of the integral of a r

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