Pustyl'nikov Lev Davidovich

Publications in Math-Net.Ru

1. On the quantum chaos conjecture and generalized continued fractions
   
   Keldysh Institute preprints, 2015, 037, 12 pp.
2. Energy Levels of Quantum Periodic Systems and Quantum Chaos
   
   Keldysh Institute preprints, 2014, 027, 8 pp.
3. Nonequilibrium gas, entropy and generalized billiards
   
   Keldysh Institute preprints, 2014, 003, 10 pp.
4. Black holes and generalized relativistic billiards
   
   Keldysh Institute preprints, 2013, 054, 36 pp.
5. Fast prediction of quasistationary processes
   
   Keldysh Institute preprints, 2012, 028, 15 pp.
6. On the classical Riemann zeta-function
   
   Keldysh Institute preprints, 2012, 027, 17 pp.
7. Fast computations associated with Toeplitz and Hankel matrices and tensors
   
   Keldysh Institute preprints, 2011, 059, 23 pp.
8. Quasistationary processes and their prediction
   
   Keldysh Institute preprints, 2011, 058, 14 pp.
9. Algebraic structures related to Toeplitz and Hankel matrices and tensors
   
   Keldysh Institute preprints, 2010, 060, 26 pp.
10. A new necessary condition for the validity of the Riemann hypothesis
    
    Keldysh Institute preprints, 2010, 054, 8 pp.
11. Discrete rotations and generalized continued fractions
    
    Keldysh Institute preprints, 2009, 044, 7 pp.
12. On the connection of the Riemann problem with properties of a dynamical system
    
    Keldysh Institute preprints, 2009, 043, 7 pp.
13. On the Riemann hypothesis for approximate zeta-function
    
    Keldysh Institute preprints, 2008, 070, 6 pp.
14. New results on the Dirichlet $L$-functions
    
    Keldysh Institute preprints, 2008, 069, 10 pp.
15. An asymptotic formula for the derivatives of the function $\xi(s,\chi)$
    
    Keldysh Institute preprints, 2007, 044, 12 pp.
16. An asymptotic formula for the derivatives of a function Taylor
    
    Keldysh Institute preprints, 2007, 043, 14 pp.
17. Some properties of Dirichlet $L$-functions associated with their nontrivial zeros
    
    Keldysh Institute preprints, 2006, 069
18. One-dimensional model of crystal extension
    
    Keldysh Institute preprints, 2006, 068
19. Nonequilibrium gas and generalized billiards
    
    Keldysh Institute preprints, 2005, 050
20. Classification of ideals of algebras of real matrices and its applications in the number theory
    
    Keldysh Institute preprints, 2005, 018
21. Геометрическая задача, связанная с обобщенными биллиардами
    
    Mat. Pros., Ser. 3, 9 (2005),  86–92
22. Generalized Newtonian periodic billiards in a ball
    
    Uspekhi Mat. Nauk, 60:2(362) (2005),  171–172
23. On a geometrical problem connected with generalized billiards
    
    Keldysh Institute preprints, 2004, 012, 21 pp.
24. On the representation of Riemann zeta-function in the critical strip over an infinite product of second-order matrics and on a dynamical system
    
    Keldysh Institute preprints, 2004, 005, 11 pp.
25. Динамические системы с упругими отражениями и механизм ускорения Ферми
    
    Mat. Pros., Ser. 3, 8 (2004),  164–180
26. 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, 59:4(358) (2004),  197–198
27. Oscillatory motions and stability problem of solutions to Hamiltonian systems with many degrees of freedom
    
    Keldysh Institute preprints, 2003, 005, 29 pp.
28. Generalized relativistic billiards
    
    Regul. Chaotic Dyn., 8:3 (2003),  283–296
29. Refutation of an analogue of the Riemann hypothesis about zeros for an arbitrarily sharp approximation of the zeta-function satisfying the same functional equation
    
    Uspekhi Mat. Nauk, 58:1(349) (2003),  175–176
30. Generalized continued fractions and ergodic theory
    
    Uspekhi Mat. Nauk, 58:1(349) (2003),  113–164
31. The quantum chaos conjecture and generalized continued fractions
    
    Mat. Sb., 194:4 (2003),  107–118
32. Singularities and bifurcations of wave front of an ellipse
    
    Keldysh Institute preprints, 2002, 033
33. The quantum chaos conjecture and generalized continued fractions
    
    Keldysh Institute preprints, 2002, 003, 17 pp.
34. Generalized continued fractions associated with the Gauss transform
    
    Uspekhi Mat. Nauk, 57:5(347) (2002),  159–160
35. Proof of the quantum chaos conjecture and generalised continued fractions
    
    Uspekhi Mat. Nauk, 57:1(343) (2002),  161–162
36. Space-Time Chaos, Critical Phenomena, and Bifurcations of Solutions of Infinite-Dimensional Systems of Ordinary Differential Equations
    
    TMF, 133:1 (2002),  36–53
37. Discrete wave equations with random parameters and a discrete string with random masses
    
    Teor. Veroyatnost. i Primenen., 47:2 (2002),  255–269
38. An asymptotic formula for the Taylor coefficients of the function $\xi(s)$
    
    Izv. RAN. Ser. Mat., 65:1 (2001),  93–106
39. The spatially-temporal chaos and the theory of infinite-dimensional systems of ordinary differential equations originating in some physical problems
    
    Keldysh Institute preprints, 2001, 044
40. Critical phenomena and bifurcations of solutions of infinite-dimensional systems of ordinary differential equations originating in some physical problems
    
    Keldysh Institute preprints, 2001, 043
41. Infinite-dimensional generalized continued fractions, sums of Legendre symbols and distribution of quadratic residues and non-residues
    
    Keldysh Institute preprints, 2001, 002
42. On analytic properties of an ellipse connected with singularities of its wave front
    
    Uspekhi Mat. Nauk, 56:5(341) (2001),  185–186
43. Probability and ergodic laws in the distribution of the fractional parts of the values of polynomials
    
    Mat. Sb., 192:2 (2001),  103–118
44. Invariant Measures for Hyperbolic Partial Differential Equation and their Applications
    
    Keldysh Institute preprints, 2000, 034
45. The asymptotics of coefficients of the Taylor series of the function $\xi(s)$
    
    Keldysh Institute preprints, 2000, 009
46. On the asymptotic behaviour of the Taylor series coefficients of $\xi(s)$
    
    Uspekhi Mat. Nauk, 55:2(332) (2000),  145–146
47. Probabilistic and Ergodic Laws in the Distribution of Fractional Parts of the Polynomials Values
    
    Keldysh Institute preprints, 1999, 048
48. Stochastic Вiscrete Wafe Differential Equations and the Discrete String with Random Masses
    
    Keldysh Institute preprints, 1999, 007
49. Probability laws in the distribution of the fractional parts of the values of polynomials and evidence for the quantum chaos conjecture
    
    Uspekhi Mat. Nauk, 54:6(330) (1999),  173–174
50. The law of entropy increase and generalized billiards
    
    Uspekhi Mat. Nauk, 54:3(327) (1999),  179–180
51. On a property of the classical zeta-function associated with the Riemann hypothesis
    
    Uspekhi Mat. Nauk, 54:1(325) (1999),  259–260
52. Generalized Continued Fractions Connected with the Gauss Transformation
    
    Keldysh Institute preprints, 1998, 035
53. On the measure of one-way oscillating motions for the Kolmogorov model and its generalization in the $n$-body problem
    
    Uspekhi Mat. Nauk, 53:5(323) (1998),  245–246
54. Generalized Continued Fractions and Differential Equations
    
    Keldysh Institute preprints, 1997, 096
55. Investigation of the Standart Map and Its Probablistic Analog
    
    Keldysh Institute preprints, 1997, 029
56. Infinite-dimensional non-linear ordinary differential equations and the KAM theory
    
    Uspekhi Mat. Nauk, 52:3(315) (1997),  105–160
57. Infinite-dimensional generalized continued fractions, quadratic residues and non-residues, and ergodic theory
    
    Uspekhi Mat. Nauk, 52:2(314) (1997),  183–184
58. Infinitely Dimensional Ordinary Differential Equations of a General Kind
    
    Keldysh Institute preprints, 1996, 084
59. Theory of an Equation with the Fermi-Pasta-Ulam Nonlinearity
    
    Keldysh Institute preprints, 1996, 055
60. Theory of an Equation with the Frenkel-Kontorova Potential
    
    Keldysh Institute preprints, 1996, 050
61. On non-unique solubility and insolubility of an analytic infinite-dimensional ordinary differential equation of chain type
    
    Uspekhi Mat. Nauk, 50:6(306) (1995),  207–208
62. Construction of periodic solutions in an infinite system of Fermi–Pasta–Ulam ordinary differential equations, stability, and KAM theory
    
    Uspekhi Mat. Nauk, 50:2(302) (1995),  221–222
63. Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism
    
    Uspekhi Mat. Nauk, 50:1(301) (1995),  143–186
64. Generalized continued fractions and estimates of Weyl sums and the remainder term in the distribution law for the fractional parts of the values of a polynomial
    
    Mat. Zametki, 56:6 (1994),  144–148
65. Existence of invariant curves for maps close to degenerate maps, and a solution of the Fermi–Ulam problem
    
    Mat. Sb., 185:6 (1994),  113–124
66. Distribution of the fractional parts of a polynomial, Weyl sums, and ergodic theory
    
    Uspekhi Mat. Nauk, 48:4(292) (1993),  131–166
67. The distribution of quadratic residues and non-residues and a dynamical system
    
    Uspekhi Mat. Nauk, 48:1(289) (1993),  179–180
68. On the spectrum of the discrete inhomogeneous wave equation, and vibrations of a discrete string
    
    Mat. Sb., 183:3 (1992),  38–54
69. Infinite-dimensional strange attractors and bifurcations in adynamical system with infinitely many degrees of freedom
    
    TMF, 92:1 (1992),  85–91
70. On the connection of the Riemann problem on zeros of the function $\zeta(s)$ with the spectrum of an operator acting in a Hilbert space
    
    Uspekhi Mat. Nauk, 46:2(278) (1991),  227–228
71. A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics
    
    TMF, 86:1 (1991),  120–129
72. A new mechanism of particle acceleration and rotation numbers
    
    TMF, 82:2 (1990),  257–267
73. A ground state in the Frenkel'-Kontorova model
    
    Funktsional. Anal. i Prilozhen., 22:1 (1988),  85–86
74. New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model
    
    TMF, 77:1 (1988),  154–160
75. On the Fermi–Ulam model
    
    Dokl. Akad. Nauk SSSR, 292:3 (1987),  549–553
76. On oscillatory motions in a certain dynamical system
    
    Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987),  1010–1032
77. Asymptotic behavior of trajectories of a standard mapping
    
    Mat. Zametki, 39:5 (1986),  719–726
78. A dynamical system with infinitely many degrees of freedom and solution of the Frenkel'–Kontorova problem
    
    TMF, 68:1 (1986),  58–68
79. Strict justification of the possibility of unbounded increase in particle energy in a problem of nuclear physics
    
    Dokl. Akad. Nauk SSSR, 283:3 (1985),  550–553
80. Toeplitz and Hankel matrices and their applications
    
    Uspekhi Mat. Nauk, 39:4(238) (1984),  53–84
81. Unbounded growth of the action variable in certain physical models
    
    Tr. Mosk. Mat. Obs., 46 (1983),  187–200
82. On Ulam's problem
    
    TMF, 57:1 (1983),  128–132
83. On a method for finding admissible controls in a linear system with phase constraints
    
    Differ. Uravn., 17:12 (1981),  2176–2184
84. On new estimates for the Weyl sums and the remainder term in the distribution of the fractional parts of a polynomial
    
    Uspekhi Mat. Nauk, 36:2(218) (1981),  203–204
85. On the algebraic structure of the spaces of Toeplitz and Hankel matrices
    
    Dokl. Akad. Nauk SSSR, 250:3 (1980),  556–559
86. On fast calculations in some problems of linear algebra connected with Toeplitz and Hankel matrices
    
    Uspekhi Mat. Nauk, 35:5(215) (1980),  241–242
87. Unbounded growth of the action variable in some physical models, and the problem of stochasticity
    
    Dokl. Akad. Nauk SSSR, 241:5 (1978),  1035–1038
88. Stable and oscillating motions in nonautonomous dynamical systems. II
    
    Tr. Mosk. Mat. Obs., 34 (1977),  3–103
89. Stable and oscillating motions in nonautonomous dynamical systems. A generalization of C. L. Siegel's theorem to the nonautonomous case
    
    Mat. Sb. (N.S.), 94(136):3(7) (1974),  407–429
90. Existence of a set of positive measure of oscillating motions in a certain problem of dynamics
    
    Dokl. Akad. Nauk SSSR, 202:2 (1972),  287–289
91. On stability of half-trajectories under area-preserving mappings of the plane
    
    Dokl. Akad. Nauk SSSR, 202:1 (1972),  38–40
92. A generalization of two theorems of C. L. Siegel to the nonautonomous case
    
    Uspekhi Mat. Nauk, 26:4(160) (1971),  245–246
93. A certain dynamical system
    
    Uspekhi Mat. Nauk, 23:4(142) (1968),  251–252