Lev Pustyl'nikov

Born:	September 7, 1946 in Moscow, U.S.S.R. Died: September 15, 2015
Citizenship:	Russia
Personal:	Married, with two children
Former Official Address:	Keldysh Institute of Applied Mathematics of RAS Miusskaja sq.4, 125047, Moscow, Russia
Telephone:	Office: (007) (095) 250-78-84. Home: (007) (095) 150-45-38 Fax: (007) (095) 972-07-37

Education

Professional

Teaching

Membership

Honour

Participation in most important conferences

[1] On a certain dynamical system, Uspehi Mat. Nauk 23, no. 4 (142), (1968), 251-252.

[2] The generalization of two theorems of K. L. Sigel to the nonautonomous case, Uspehi Mat. Nauk, 26, no. 4 (160), (1971), 247-248.

[3] On the stability of half-trajectories under area-preserving mappings of the plane, Dokl. Akad.
Nauk SSSR 22, no. 1, (1972), 38-40.

[4] Existance of a set of positive measure of oscillating motions in a certain problem of dynamics, Dokl. Akad. Nauk, SSSR, 202, no. 2, (1972), 287-289.

[5] Stable and oscillating motions in nonautonomous dynamical systems, Math. Sb. 94 (136) (1974), 407-429.

[6] Stable and oscillating motions in nonautonomous dynamical systems II, Trudy Moskov. Mat. Obsc. 34, (1977), 3-103.

[7] On the method of determination of control actions in ARFP and on construction of nonlinear model of the object of regulation, Trudy of Institute ``Power Systems and Electric Power Networks", V. 9 (1977), 83-94.

[8] On optimal ordering tasks to be done by two users (with T.V. Lokot'), Collection of works of Moscow Institute for engineering and construction, N153 (1977), 197-202.

[9] Unbounded growth of an action variable in some physical models and the stochastic problem, Dokl. Akad. Nauk SSSR, 241, N5 (1978), 1035-1038.

[10] The algebraic structure of the space of Toeplitz and Hankel matrices, Dokl. Akad. Nauk SSSR 250 (1980), 556-559.

[11] Fast computations in some problems of linear algebra connected with Toeplitz and Hankel matrices, Uspekhi Mat. Nauk 35:5 (1980), 241-242.

[12] A method of finding admissible controls in a linear system with phase restrictions, Differential equations, Vol. 17, number 12 (1981), 2176-2184.

[13] New estimates of Weyl sums and the remainder term in the law of distribution of fractional parts of a polynomial, Uspekhi Math. Nauk 36 (2) (1981), 203-204.

[14] On the method of identification of the object of regulation with unknown entoring information, Systems of automatized control in energetics. Collection of scientific works of Institute ``Power Systems and Electric Networks", (1982), 90-98. M.

[15] Unbounded growth of an action variable in some physical models, Trudy Moskov. Mat. Obshch. 46 (1983), 187-200.

[17] On a problem of correction of an operating condition of power system for active power, Collection of scientific works of Institute ``Power Systems and Electric Networks", (1983), 39-45. M.

[18] Toeplitz and Hankel matrices and their application, Uspekhi Mat. Nauk 39:4 (1984), 53-84.

[19] Apparatus of correction of an operating condition of power system for active power, Author certificate N3390090/24-07, bulletin N22 (in Russia).

[20] On a rigorous proof of the possibility of unbounded growth of particle energy in a problem of nuclear physics, Dokl. Akad. Nauk SSSR 283 (1985), 550-553.

[21] Apparatus of optimal distribution of active powers in energetic systems (with M.I. Londer, V.A. Morosov, T.A. Rudakova), Author certificate N3414983/24-07, bulletin N14 (in Russia).

[22] On asymptotial behaviour of the trajectories of the standard map, Matem. Sametki, 39, N5 (1986), 719-726.

[23] On a mathematical method of optimal distribution of active powers in energetic system, Development, design and introduction of technical tools ASC in energetics. Collection of scientific works of Institute ``Power Systems and Electric Networks", (1986), 94-107. M.

[24] Applications of method of optimal distribution of active powers for determination of twenty-four hours operating conditions in two energetic systems, Development, design and introduction of technical tools ASC in energetics. Collection of scientific works of Institute ``Power Systems and Electric Networks ", (1986), 108-121. M.

[25] On a dynamical system with infinite number of degrees of freedom and solutions of the Frenkel-Kontorova problem, Teor. Mat. Fiz, 68, N1 (1986), 58-68.

[26] Method of regulation of frequency and active power, Izvestiya Akad. Nauk SSSR, energetika and transport, N6 (1986), 16-24.

[28] On oscillatory motions in a certain dynamical system, Izvestiya Akad. Nauk SSSR, Series mathematics, 51, N5 (1987), 1010-1032.

[29] On one ground state in the Frenkel-Kontorova model, Function. analysis and it's applications, 22, N1 (1988), 85-86.

[30] New mechanism of particle acceleration and relativistic analog of the Fermi-Ulam model, Teor. Mat. Fiz., 77, N1 (1988), 154-160.

[31] Parallel computations with Toeplitz and Hankel matrices (with T.V. Lokot'), Cybernetics and computing techniques, issue 4 (1988), 96-121.

[32] On formulas for determination of torsional rigidity of the split phase taking the deflection of conductors in account, Deposited scientific works, N2 (1989), 159.

[33] A new mechanism of particle acceleration and rotation numbers, Teor. Mat. Fiz., 82, N2 (1990), 257-267.

[34] On certain final motions in the n-body problem, Prikl. Matem. Mekhan., 54, N2 (1990), 329-331.

[35] A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics, 86, N1 (1991), 120-129.

[36] On the connection of the Rieman problem on zeros of the function $\zeta (s)$ with the spectrum of an operator acting in a Hilbert space, Uspehi Mat. Nauk, N2 (1991).

[37] Aerodynamic unstable vibrations of conductors of air line of electrotransmission with ice deflections (with V.A. Shkaptsov), Izvestiya Akad. Nauk SSSR, energetika and transport, N2 (1991), 103-109.

[38] Air line of electrotransmission (with V.A. Shkaptsov and A.F. Golubev), Author certificate N4611172/24-07, bulletin N39 (in Russia).

[39] New estimates of Weyl sums and the remainder term in the law of distribution of the fractional part of a polynomial, Ergodic Theory and Dynamical systems 11 (1991), 515-534.

[40] On the spectrum of the discrete non-homogenous wave equation and oscillation of the discret string, Mat. sbornik, 183, N3 (1992), 38-54.

[41] Infinite dimensional strange attractors and bifurcations in dynamical system with infinite number of degrees of freedom, Teor. Mat. Fiz., 92, N1 (1992), 85-91.

[42] Bundle of split conductors of air line electrotransmission with pendulum for extinguishing of vibrations (with V.A. Shkaptsow, V.A. Shereshevskii and A.F. Golubev), Patent N1631649 (in Russia).

[43] Airline of electrotransmission (with V.A. Shkaptsov and V.A. Shereshevskii), Author certificate N1725310 (in Russia).

[44] The method of extinguishing of galloping conductors (with V.A. Shkaptsov), Izvestiya Akad. Nauk, energetika, N6 (1992), 74-81.

[45] On distribution of quadratic residues and non-residues and on a certain dynamical system, Uspekhi Mat. Nauk, N1 (1993), 179-180.

[46] The distribution of the fractional part of a polynomial value, the Weyl sums and ergodic theory, Uspekhi Mat. Nauk, N4 (1993), 131-166; english translation in Russian Math. Surveys, vol. 48, N 4 (1993), p. 143-179.

[47] The existance of invariant curves for mappings close to degenerate ones, and the solutions of the Fermi-Ulam problem, Mat. Sb. 185: 6 (1994), 1-12; English transl. in Russia Acad. Sci. Sb.
Math. 82 (1995).

[48] On the estimates of Weyl sums (with J. Schmeling), Preprint No. 9, Inst. für Angewandte Analysis und Stochastik, Berlin, 1994.

[49] Ergodic Theory and Some Number Theory Problem. Preprint, Forschungsinstitut für Mathematik, ETH Zürich, July 1994.

[50] The generalized continued fractions and the estimates of Weyl sums and remainder term in the law of distribution of fractional parts of the values of a polynomial, Matem. Sametki (1994), Vol. 56, N. 6, 144-148; english transl. in Mathematical Notes, Vol. 56, N 5-6, p. 1315-1317.

[51] On a Ground State in the Frenkel-Kontorova Model and Metric Properties of Mappings of Standard Type, Advances in Soviet Mathematics (1994), Vol. 20, p. 277-289.

[52] A model of Poincaré and rigorous proof of the second element of thermodynamics from mechanics, Hamiltonian Mechanics Integrability and Chaotic Behavior, Plenum Press New York and London, p. 295-297.

[53] Poincaré model, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism, Uspekhi Mat. Nauk (1995), 50: 1, 143-186; english transl. in Russian Math. Surveys (1995), 50: 1, p. 145-189.

[54] Construction of periodic solutions in an infinite system of Fermi-Pasta-Ulam ordinary differential equations, stability, and KAM-theory; Uspekhi Mat. Nauk (1995), 50: 2, 221-222; english transl. in Russian Math. Surveys (1995), Vol. 50, N. 2, p. 449-450.

[55] On the stability of solutions and absence of Arnold's diffusion in a nonintegrable Hamiltonian system of a general form with three degrees of freedom. Preprint Weierstraß-Institut für Angewandte Analysis and Stochstic; No. 155, Berlin, 1995.

[56] Acceleration of bouncing ball in external fields (with T. Krüger and S.E. Troubetzkoy), Nonlinearity 8 (1995), p. 397-410.

[57] On non-unique solubility and insolubility of an analytic infinite-dimensional ordinary differential equation of chain type, Uspekhi Mat. Nauk (1995), 50: 6, 207-208; english transl. in Russian Math. Surveys (1995), 50: 6, 1297-1298.

[58] On some solutions of infinite-dimensional system of ordinary differential equations originating in statistical mechanics (with T.V. Lokot'), Sinai's Moscow Seminar on Dynamical Systems, Advances in the Mathematical Sciences. AMS Translations. Series 2, Vol. 171, 1996, p. 173-183.

[59] Theory of an equation with the Frenkel-Kontorova potential, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N 50, Moscow, 1996.

[60] Theory of an equation with the Fermi-Pasta-Ulam nonlinearity, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N 55, Moscow, 1996.

[61] Infinitely dimensional ordinary differential equations of a general kind, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N 84, Moscow, 1996.

[62] The nonautonomous function-theoretic center problem (with T. Krüger and S. Troubetzkoy) BiBoS-Preprint No. 760/2/97, Universität Bielefeld, 1997.

[63] A KAM type theorem for systems with round-off errors, (with M. Blank and T. Krüger) BiBoS-Preprint, No. 765/3/97, Universität Bielefeld, 1997.

[64] Infinitely dimensional continued fractions, the distribution of quadratic residues and non-residues and ergodic theory, Uspekhi Mat. Nauk N 2 (1997), 183-184.

[65] Infinitely dimensional nonlinear ordinary differential equations and KAM-theory, Uspekhi Mat. Nauk, N 3(1997)105-160; english transl. in Russian Math. Surveys (1997), 52:3, 551-604.

[66] Investigation of the standard map and its probabilistic analog, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N29, Moscow, 1997.

[67] Generalized continued fractions and differential equations, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N96, Moscow, 1997.

[69] Generalized continued fractions connected with Gauss transformations, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N35, Moscow, 1998.

[70] The nonautonomous function-theoretic center problem (with T. Krüger and S. Troubetzkoy), Bol. Soc. Bras. Mat.,(1999),vol.30,N.1,1-30.

[71] On a measure of one-sided oscillatory motions in the model of A.N. Kolmogorov and in its generalization in n-body problem, Uspekhi Mat. Nauk, (1998), N.5, 245-246; English translation in Russian Math. Surveys 53 (1998), 1102-1103.

[72] Generalized continued fractions and ergodic theory, Journal of Mathematical Sciences, (1999), 95, 2552-2563.

[73] On a property of the classical zeta-function associated with the Riemann hypothesis, Uspekhi Mat. Nauk, (1999), 54:1, 260-261;english translation in Russian Math. Surveys (1999), 54:1,262-263.

[74] The law of entropy increase and generalized billiards, Uspekhi Mat.Nauk, (1999),54:3, 654-655;english translation in Russian Math.Surveys (1999), 54:1, 650-651.

[75] Probability laws in the fractional parts of the values of polynomials and evidence for the quantum chaos conjecture, Uspekhi Mat.Nauk,(1999), 54:6; english translation in Russian Math.Surveys (1999), 54:6, 1259-1260.

[76] The random discrete string (S.Albeverio), BiBoS-Preprint,Nr.832/1/99, Universitat Bielefeld, 1999.

[77] Infinite-dimensional generalized continued fractions, distribution of quadratic residues and non-residues and ergodic theory, BiBoS-Preprint,Nr.99-09-08, Universitat Bielefeld, 1999.

[78] Stochastic discrete wave equations and a discrete string with random masses, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.7, Moscow, 1999.

[79] Probabilistic and ergodic laws in the distribution of fractional parts of the polynomial values,Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.48, Moscow, 1999.

[80] The asymptotic of the Taylor series coefficients of the function $\xi(s)$ , Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.49, Moscow, 2000.

[81] On the asymptotic behavior of the Taylor series coefficients of the function $\xi(s)$ , Uspekhi Mat.Nauk,(2000), 55:2, 349-350; english translation in Russian Math.Surveys (2000),55:2, 349-350.

[82] The standard map and a Probabilistic Conjecture, Math.Nachr. 219 (2000), 181-187.

[83] Invariant measures for hyperbolic partial differential equation and their applications,Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.34, Moscow, 2000.

[84] An asymptotic formula for the Taylor coefficients of the function $\xi(s)$ , Izvestya RAN:Ser.Mat (2001), 65:1, 93-106; english translation in Izvestia:Mathematics, (2001), 65:1, 85-98.

[85] Probability and ergodic laws in the distribution of fractional parts of the values of polynomials, Matematicheskii Sbornik, (2001), 192:2, 103-118; english translation in Sbornik:Mathematics,

[86] Critical phenomena and strange attrators for some infinite-dimensional physical systems ( with Ph.Blanchard), BiBoS-Preprint,Nr.01-01-030,Universitat Bielefeld,2001.

[87] Bifurcations and critical phenomena for some infinite-dimensional physical systems ( with Ph.Blanchard), BiBoS-Preprint, Nr.01-05-038, Universitat Bielefeld, 2001.

[88] Yhe proof of quantum chaos conjecture, the distribution of distances between adjacent fractionalparts of polynomial values, and generalized continuous fractions, BiBoS-Preprint, Nr.01-06-040, Universitat Bielefeld, 2001.

[89] Critical phenomena and analytic properties of an ellipse connected with singularities of its wave front, BiBoS-Preprint, Nr.01-07-050, Universitat Bielefeld, 2001.

[90] Critical phenomena and bifurcations of solutions of infinite-dimensional systems of ordinary diffential equations appearing in some physical problems, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.43,Moscow,2001.

[91] Space -time chaos and the theory of infinite-dimensional systems of ordinary diffential equations appearing in some physical problems, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.44,Moscow, 2001.

[92] On analytic properties of an ellipse connected with singularities of its wave front, Uspekhi Mat.Nauk,(2001),56:5,185-186;english translation in Russian Math.Surveys (2001), 56:5, 984-985.

[93] Critical phenomena and analytic properties of an ellipse connected with singularities of its wave front,Proceedings of the Workshop "The Science of Complexity: From Mathematics to Technology to a Sustainable World", No 2001/058, Bielefeld, 2001; available at http://www.physik.uni-bielefeld.de/complexity/publications_html

[94] Poisson law distribution in subset surprisology (with A.Dress and T.Lokot), Proceedings of the Workshop "The Science of Complexity: From Mathematics to Technology to a Sustainable World", No 2001/105, Bielefeld, 2001; available at http://www.physik.uni-bielefeld.de/complexity/publications_html

[95] Infinite-dimensional generalized continued fractions, sums of Legendre symbols and distribution of quadratic residues and non-residues, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.2, Moscow, 2001.

[96] Proof of quantum chaos conjecture, and generalized continuous fractions, Uspekhi Mat.Nauk,

(2002), 57:1, 161-162; english translation in Russian Math.Surveys (2002), 57:1, 159-160.

[97] The quantum chaos conjecture and generalized continued fractions, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.3, Moscow, 2002.

[98] Singularities and bifurcations of wave front of an ellipse, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.33, Moscow, 2002.

[99] Prediction of Quasistationary procesees, Complexity, and Toeplitz Matrics 1, BiBoS-Preprint,

[100] Generalized relativistic billiards in external force fields (with M.V.Deryabin), BiBoS-Preprint, Nr.02-06-091, Universitat Bielefeld, 2002.

[101] Discrete wave equations with random parameters and a discrete string with random masses, Teorija verojatn. i primenenija,(2002), vol.47, No.2; english translation in Theory Probab.

[102] Space -time chaos, critical phenomena and bifurcations of solutions of infinite-dimensional systems of ordinary diffential equations, Teoreticheskja i Matematicheskja Fizika,(2002), vol.133, No.1,36-53; english translation in Theoret. and Math.Physics, (2002), 133(1), 1348-1362.

[103] Generalized continuous fractions associated with the Gauss transform, Uspekhi Mat.Nauk,

(2002), 57:5;english translation in Russian Math.Surveys (2002), 57:5, 1005-1006.

[104] Infinite-dimensional generalized continued fractions, distribution of quadratic residues and non-residues, and ergodic theory, Infinite Analysis, Quantum Probability and Related Topics, (2002), vol.5, No.4, 555-570.

[105] Central limit theorem for a probability approximation of the standard map, BiBoS-Preprint,

[106] Generalized continued fractions and ergodic theory, Uspekhi Mat.Nauk,(2003),58:1,113-164;

[107] Refutation of an analogue of Riemann hypothesis about zeros for an arbitrarily sharp approximation of the zeta-function satisfying the same functional equation, Uspekhi Mat.Nauk, (2003),58:1, 175-176;english translation in Russian Math.Surveys (2003), 58:1, 193-194.

[108] Oscillatory motions and stability problem of solutions of Hamiltonian systems with many degrees of freedom, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.5, Moscow, 2003.

[109] The quantum chaos conjecture and generalized continued fractions, Matematicheskii Sbornik, (2003), 194:4, 107-118; english translation in Sbornik:Mathematics,(2003), 194:4, 575-587.

[110] On generalized relativistic billiards in external force fields (with M.V.Deryabin), Letters in Math. Physics, (2003), 63, 195-207.

[111] A new scale-invariant geometry on

spaces (with A.Dress and T.Lokot), Preprint, Forscdhungsschwerpunkt Mathematisierung-Dynamik and Striktur komplexer No.155, Universitat Bielefeld, 2003.

[112] Generalized relativistic billiards (with M.V.Deryabin), Regular and Chaotic Dynamics,(2003), v.8, N.3, 283-296.

[113] A representation of the Riemann zeta-function in the critical strip by means of an infinite product of matrices of order two, and a certain dynamical system, Preprint of the Keldysh Institute of Applied Mathematics of RAS, N.5, Moscow, 2004.

[114] The quantum chaos conjecture,Proceedings of the Workshop "Noncommutative algebra 2003": Selected Problems,available

[115] The Law of Entropy Increase and Generalized Relativistic Billiards, BiBoS-Preprint, Nr.04-02-139, Universitat Bielefeld, 2004.

[116] Dynamical systems with elastic reflection and Fermi acceleration mechanism, Matematicheskoe Prosveschenie, N.8 (2004),164-180.

[117] Stable oscillatory motions in accelerator model of charge particles, Trudy Mos. Mat. Obschestva, T.65 (2004),english.transl. in Trans.Moscow Math. Soc.,V.65 (2004),1-35.

[118] On a geometrical problem connected with generalized billiards, Preprint of the Keldysh Institute of Applied Mathematics of RAS,N.12, Moscow, 2004.

[119] A new scale-invariant geometry on

spaces (with A.Dress and T.Lokot), Applied Math. Letters,17 (2004),815-820.

[120] A representation of the Riemann zeta-function in the critical strip by means of an infinite product of matrices of order two, and a certain dynamical system, Uspekhi Mat.Nauk, (2004),59:4;english translation in Russian Math.Surveys (2004), 59:4, 796-797.

[121] Large deviations in discrete rotation maps (with T.Lokot and R.Pustylnikov) BiBoS-Preprint, Nr.04-05-143, Universitat Bielefeld, 2004.

[122] Large deviations in discrete rotation maps (with T.Lokot and R.Pustylnikov) Proceedings of the Seventh International Workshop on Computer Algebra in Scientific Computing,Juli 12-19,2004,St.Petersburg,Russia, 379-382.

[123] Poisson numbers and Poisson distributions in subset surprisdlogy (with A.Dress, T.Lokot and W. Schubert), Annals of Combinatorics 8 (2004) 473-485.

[124] Exponential attractors in generalized relativistic billiards (with.M.V.Derybin) , Comm.Math. Physics, 248, N.3 (2004), 527-552.

Prof. Dr. Lev Pustyl'nikov

Curriculum Vitae