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Publications in Math-Net.Ru |
Citations |
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2015 |
1. |
L. D. Pustyl'nikov, “On the quantum chaos conjecture and generalized continued fractions”, Keldysh Institute preprints, 2015, 037, 12 pp. |
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2014 |
2. |
L. D. Pustyl'nikov, “Energy Levels of Quantum Periodic Systems and Quantum Chaos”, Keldysh Institute preprints, 2014, 027, 8 pp. |
3. |
L. D. Pustyl'nikov, M. V. Deryabin, “Nonequilibrium gas, entropy and generalized billiards”, Keldysh Institute preprints, 2014, 003, 10 pp. |
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2013 |
4. |
L. D. Pustyl'nikov, M. V. Deryabin, “Black holes and generalized relativistic billiards”, Keldysh Institute preprints, 2013, 054, 36 pp. |
1
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2012 |
5. |
L. D. Pustyl’nikov, “Fast prediction of quasistationary processes”, Keldysh Institute preprints, 2012, 028, 15 pp. |
6. |
L. D. Pustyl’nikov, “On the classical Riemann zeta-function”, Keldysh Institute preprints, 2012, 027, 17 pp. |
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2011 |
7. |
L. D. Pustyl’nikov, T. V. Lokot', “Fast computations associated with Toeplitz and Hankel matrices and tensors”, Keldysh Institute preprints, 2011, 059, 23 pp. |
8. |
L. D. Pustyl’nikov, “Quasistationary processes and their prediction”, Keldysh Institute preprints, 2011, 058, 14 pp. |
1
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2010 |
9. |
L. D. Pustyl’nikov, T. V. Lokot', “Algebraic structures related to Toeplitz and Hankel matrices and tensors”, Keldysh Institute preprints, 2010, 060, 26 pp. |
4
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10. |
L. D. Pustyl’nikov, “A new necessary condition for the validity of the Riemann hypothesis”, Keldysh Institute preprints, 2010, 054, 8 pp. |
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2009 |
11. |
L. D. Pustyl'nikov, T. V. Lokot', “Discrete rotations and generalized continued fractions”, Keldysh Institute preprints, 2009, 044, 7 pp. |
12. |
L. D. Pustyl'nikov, “On the connection of the Riemann problem with properties of a dynamical system”, Keldysh Institute preprints, 2009, 043, 7 pp. |
1
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2008 |
13. |
L. D. Pustyl'nikov, “On the Riemann hypothesis for approximate zeta-function”, Keldysh Institute preprints, 2008, 070, 6 pp. |
2
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14. |
L. D. Pustyl'nikov, T. V. Lokot', “New results on the Dirichlet $L$-functions”, Keldysh Institute preprints, 2008, 069, 10 pp. |
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2007 |
15. |
L. D. Pustyl’nikov, “An asymptotic formula for the derivatives of the function $\xi(s,\chi)$”, Keldysh Institute preprints, 2007, 044, 12 pp. |
1
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16. |
L. D. Pustyl'nikov, T. V. Lokot', “An asymptotic formula for the derivatives of a function Taylor”, Keldysh Institute preprints, 2007, 043, 14 pp. |
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2006 |
17. |
L. D. Pustyl'nikov, “Some properties of Dirichlet $L$-functions associated with their nontrivial zeros”, Keldysh Institute preprints, 2006, 069 |
1
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18. |
L. D. Pustyl'nikov, V. A. Malyshev, “One-dimensional model of crystal extension”, Keldysh Institute preprints, 2006, 068 |
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2005 |
19. |
L. D. Pustyl'nikov, “Nonequilibrium gas and generalized billiards”, Keldysh Institute preprints, 2005, 050 |
20. |
L. D. Pustyl’nikov, “Classification of ideals of algebras of real matrices and its applications in the number theory”, Keldysh Institute preprints, 2005, 018 |
21. |
L. D. Pustyl'nikov, “Ãåîìåòðè÷åñêàÿ çàäà÷à, ñâÿçàííàÿ ñ îáîáùåííûìè áèëëèàðäàìè”, Mat. Pros., Ser. 3, 9 (2005), 86–92 |
22. |
L. D. Pustyl'nikov, “Generalized Newtonian periodic billiards in a ball”, Uspekhi Mat. Nauk, 60:2(362) (2005), 171–172 ; Russian Math. Surveys, 60:2 (2005), 365–366 |
1
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2004 |
23. |
L. D. Pustyl’nikov, “On a geometrical problem connected with generalized billiards”, Keldysh Institute preprints, 2004, 012, 21 pp. |
24. |
L. D. Pustyl’nikov, “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. |
L. D. Pustyl'nikov, “Äèíàìè÷åñêèå ñèñòåìû ñ óïðóãèìè îòðàæåíèÿìè è ìåõàíèçì óñêîðåíèÿ Ôåðìè”, Mat. Pros., Ser. 3, 8 (2004), 164–180 |
26. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 59:4 (2004), 796–797 |
1
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2003 |
27. |
L. D. Pustyl’nikov, “Oscillatory motions and stability problem of solutions to Hamiltonian systems with many degrees of freedom”, Keldysh Institute preprints, 2003, 005, 29 pp. |
28. |
M. V. Deryabin, L. D. Pustyl'nikov, “Generalized relativistic billiards”, Regul. Chaotic Dyn., 8:3 (2003), 283–296 |
8
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29. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 58:1 (2003), 193–194 |
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30. |
L. D. Pustyl'nikov, “Generalized continued fractions and ergodic theory”, Uspekhi Mat. Nauk, 58:1(349) (2003), 113–164 ; Russian Math. Surveys, 58:1 (2003), 109–159 |
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31. |
L. D. Pustyl'nikov, “The quantum chaos conjecture and generalized continued fractions”, Mat. Sb., 194:4 (2003), 107–118 ; Sb. Math., 194:4 (2003), 575–587 |
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2002 |
32. |
L. D. Pustyl'nikov, “Singularities and bifurcations of wave front of an ellipse”, Keldysh Institute preprints, 2002, 033 |
33. |
L. D. Pustyl'nikov, “The quantum chaos conjecture and generalized continued fractions”, Keldysh Institute preprints, 2002, 003, 17 pp. |
34. |
L. D. Pustyl'nikov, “Generalized continued fractions associated with the Gauss transform”, Uspekhi Mat. Nauk, 57:5(347) (2002), 159–160 ; Russian Math. Surveys, 57:5 (2002), 1005–1006 |
1
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35. |
L. D. Pustyl'nikov, “Proof of the quantum chaos conjecture and generalised continued fractions”, Uspekhi Mat. Nauk, 57:1(343) (2002), 161–162 ; Russian Math. Surveys, 57:1 (2002), 159–160 |
3
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36. |
L. D. Pustyl'nikov, “Space-Time Chaos, Critical Phenomena, and Bifurcations of Solutions of Infinite-Dimensional Systems of Ordinary Differential Equations”, TMF, 133:1 (2002), 36–53 ; Theoret. and Math. Phys., 133:1 (2002), 1348–1362 |
37. |
L. D. Pustyl'nikov, “Discrete wave equations with random parameters and a discrete string with random masses”, Teor. Veroyatnost. i Primenen., 47:2 (2002), 255–269 ; Theory Probab. Appl., 47:2 (2003), 257–268 |
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2001 |
38. |
L. D. Pustyl'nikov, “An asymptotic formula for the Taylor coefficients of the function $\xi(s)$”, Izv. RAN. Ser. Mat., 65:1 (2001), 93–106 ; Izv. Math., 65:1 (2001), 85–98 |
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39. |
L. D. Pustyl’nikov, “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. |
L. D. Pustyl’nikov, “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. |
L. D. Pustyl’nikov, “Infinite-dimensional generalized continued fractions, sums of Legendre symbols and distribution of quadratic residues and non-residues”, Keldysh Institute preprints, 2001, 002 |
42. |
L. D. Pustyl'nikov, “On analytic properties of an ellipse connected with singularities of its wave front”, Uspekhi Mat. Nauk, 56:5(341) (2001), 185–186 ; Russian Math. Surveys, 56:5 (2001), 984–985 |
43. |
L. D. Pustyl'nikov, “Probability and ergodic laws in the distribution of the fractional parts of the values of polynomials”, Mat. Sb., 192:2 (2001), 103–118 ; Sb. Math., 192:2 (2001), 261–276 |
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2000 |
44. |
L. D. Pustyl’nikov, “Invariant Measures for Hyperbolic Partial Differential Equation and their Applications”, Keldysh Institute preprints, 2000, 034 |
45. |
L. D. Pustyl'nikov, “The asymptotics of coefficients of the Taylor series of the function $\xi(s)$”, Keldysh Institute preprints, 2000, 009 |
1
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46. |
L. D. Pustyl'nikov, “On the asymptotic behaviour of the Taylor series coefficients of $\xi(s)$”, Uspekhi Mat. Nauk, 55:2(332) (2000), 145–146 ; Russian Math. Surveys, 55:2 (2000), 349–350 |
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1999 |
47. |
L. D. Pustyl’nikov, “Probabilistic and Ergodic Laws in the Distribution of Fractional Parts of the Polynomials Values”, Keldysh Institute preprints, 1999, 048 |
48. |
L. D. Pustyl’nikov, “Stochastic Âiscrete Wafe Differential Equations and the Discrete String with Random Masses”, Keldysh Institute preprints, 1999, 007 |
49. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 54:6 (1999), 1259–1260 |
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50. |
L. D. Pustyl'nikov, “The law of entropy increase and generalized billiards”, Uspekhi Mat. Nauk, 54:3(327) (1999), 179–180 ; Russian Math. Surveys, 54:3 (1999), 650–651 |
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51. |
L. D. Pustyl'nikov, “On a property of the classical zeta-function associated with the Riemann hypothesis”, Uspekhi Mat. Nauk, 54:1(325) (1999), 259–260 ; Russian Math. Surveys, 54:1 (1999), 262–263 |
10
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1998 |
52. |
L. D. Pustyl’nikov, “Generalized Continued Fractions Connected with the Gauss Transformation”, Keldysh Institute preprints, 1998, 035 |
53. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 53:5 (1998), 1102–1103 |
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1997 |
54. |
L. D. Pustyl’nikov, “Generalized Continued Fractions and Differential Equations”, Keldysh Institute preprints, 1997, 096 |
55. |
L. D. Pustyl’nikov, “Investigation of the Standart Map and Its Probablistic Analog”, Keldysh Institute preprints, 1997, 029 |
56. |
L. D. Pustyl'nikov, “Infinite-dimensional non-linear ordinary differential equations and the KAM theory”, Uspekhi Mat. Nauk, 52:3(315) (1997), 105–160 ; Russian Math. Surveys, 52:3 (1997), 551–604 |
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57. |
L. D. Pustyl'nikov, “Infinite-dimensional generalized continued fractions, quadratic residues and non-residues, and ergodic theory”, Uspekhi Mat. Nauk, 52:2(314) (1997), 183–184 ; Russian Math. Surveys, 52:2 (1997), 420–421 |
3
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1996 |
58. |
L. D. Pustyl’nikov, “Infinitely Dimensional Ordinary Differential Equations of a General Kind”, Keldysh Institute preprints, 1996, 084 |
59. |
L. D. Pustyl’nikov, “Theory of an Equation with the Fermi-Pasta-Ulam Nonlinearity”, Keldysh Institute preprints, 1996, 055 |
60. |
L. D. Pustyl’nikov, “Theory of an Equation with the Frenkel-Kontorova Potential”, Keldysh Institute preprints, 1996, 050 |
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1995 |
61. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 50:6 (1995), 1297–1298 |
1
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62. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 50:2 (1995), 449–450 |
4
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63. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 50:1 (1995), 145–189 |
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1994 |
64. |
L. D. Pustyl'nikov, “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 ; Math. Notes, 56:6 (1994), 1315–1317 |
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65. |
L. D. Pustyl'nikov, “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 ; Russian Acad. Sci. Sb. Math., 82:1 (1995), 231–241 |
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1993 |
66. |
L. D. Pustyl'nikov, “Distribution of the fractional parts of a polynomial, Weyl sums, and ergodic theory”, Uspekhi Mat. Nauk, 48:4(292) (1993), 131–166 ; Russian Math. Surveys, 48:4 (1993), 143–179 |
10
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67. |
L. D. Pustyl'nikov, “The distribution of quadratic residues and non-residues and a dynamical system”, Uspekhi Mat. Nauk, 48:1(289) (1993), 179–180 ; Russian Math. Surveys, 48:1 (1993), 185–186 |
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1992 |
68. |
L. D. Pustyl'nikov, “On the spectrum of the discrete inhomogeneous wave equation, and vibrations of a discrete string”, Mat. Sb., 183:3 (1992), 38–54 ; Russian Acad. Sci. Sb. Math., 75:2 (1993), 317–331 |
2
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69. |
L. D. Pustyl'nikov, “Infinite-dimensional strange attractors and bifurcations in adynamical system with infinitely many degrees of freedom”, TMF, 92:1 (1992), 85–91 ; Theoret. and Math. Phys., 92:1 (1992), 754–758 |
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1991 |
70. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 46:2 (1991), 255–257 |
3
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71. |
L. D. Pustyl'nikov, “A mechanism of irreversibility and unbounded growth of the energy in a model of statistical mechanics”, TMF, 86:1 (1991), 120–129 ; Theoret. and Math. Phys., 86:1 (1991), 82–89 |
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1990 |
72. |
L. D. Pustyl'nikov, “A new mechanism of particle acceleration and rotation numbers”, TMF, 82:2 (1990), 257–267 ; Theoret. and Math. Phys., 82:2 (1990), 180–187 |
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1988 |
73. |
L. D. Pustyl'nikov, “A ground state in the Frenkel'-Kontorova model”, Funktsional. Anal. i Prilozhen., 22:1 (1988), 85–86 ; Funct. Anal. Appl., 22:1 (1988), 74–75 |
74. |
L. D. Pustyl'nikov, “New mechanism of particle acceleration and relativistic analog of the Fermi–Ulam model”, TMF, 77:1 (1988), 154–160 ; Theoret. and Math. Phys., 77:1 (1988), 1110–1115 |
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1987 |
75. |
L. D. Pustyl'nikov, “On the Fermi–Ulam model”, Dokl. Akad. Nauk SSSR, 292:3 (1987), 549–553 |
7
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76. |
L. D. Pustyl'nikov, “On oscillatory motions in a certain dynamical system”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 1010–1032 ; Math. USSR-Izv., 31:2 (1988), 325–347 |
3
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1986 |
77. |
L. D. Pustyl'nikov, “Asymptotic behavior of trajectories of a standard mapping”, Mat. Zametki, 39:5 (1986), 719–726 ; Math. Notes, 39:5 (1986), 395–399 |
1
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78. |
L. D. Pustyl'nikov, “A dynamical system with infinitely many degrees of freedom and solution of the Frenkel'–Kontorova problem”, TMF, 68:1 (1986), 58–68 ; Theoret. and Math. Phys., 68:1 (1986), 673–681 |
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1985 |
79. |
L. D. Pustyl'nikov, “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 |
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1984 |
80. |
L. D. Pustyl'nikov, “Toeplitz and Hankel matrices and their applications”, Uspekhi Mat. Nauk, 39:4(238) (1984), 53–84 ; Russian Math. Surveys, 39:4 (1984), 63–98 |
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1983 |
81. |
L. D. Pustyl'nikov, “Unbounded growth of the action variable in certain physical models”, Tr. Mosk. Mat. Obs., 46 (1983), 187–200 |
7
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82. |
L. D. Pustyl'nikov, “On Ulam's problem”, TMF, 57:1 (1983), 128–132 ; Theoret. and Math. Phys., 57:1 (1983), 1035–1038 |
61
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1981 |
83. |
L. D. Pustyl'nikov, “On a method for finding admissible controls in a linear system with phase constraints”, Differ. Uravn., 17:12 (1981), 2176–2184 |
84. |
L. D. Pustyl'nikov, “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 ; Russian Math. Surveys, 36:2 (1981), 195–196 |
3
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1980 |
85. |
L. D. Pustyl'nikov, “On the algebraic structure of the spaces of Toeplitz and Hankel matrices”, Dokl. Akad. Nauk SSSR, 250:3 (1980), 556–559 |
6
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86. |
L. D. Pustyl'nikov, “On fast calculations in some problems of linear algebra connected with Toeplitz and Hankel matrices”, Uspekhi Mat. Nauk, 35:5(215) (1980), 241–242 ; Russian Math. Surveys, 35:5 (1980), 271–272 |
6
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1978 |
87. |
L. D. Pustyl'nikov, “Unbounded growth of the action variable in some physical models, and the problem of stochasticity”, Dokl. Akad. Nauk SSSR, 241:5 (1978), 1035–1038 |
1
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1977 |
88. |
L. D. Pustyl'nikov, “Stable and oscillating motions in nonautonomous dynamical systems. II”, Tr. Mosk. Mat. Obs., 34 (1977), 3–103 |
5
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1974 |
89. |
L. D. Pustyl'nikov, “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 ; Math. USSR-Sb., 23:3 (1974), 382–404 |
12
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1972 |
90. |
L. D. Pustyl'nikov, “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 |
4
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91. |
L. D. Pustyl'nikov, “On stability of half-trajectories under area-preserving mappings of the plane”, Dokl. Akad. Nauk SSSR, 202:1 (1972), 38–40 |
2
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1971 |
92. |
L. D. Pustyl'nikov, “A generalization of two theorems of C. L. Siegel to the nonautonomous case”, Uspekhi Mat. Nauk, 26:4(160) (1971), 245–246 |
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1968 |
93. |
L. D. Pustyl'nikov, “A certain dynamical system”, Uspekhi Mat. Nauk, 23:4(142) (1968), 251–252 |
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Organisations |
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