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Колебательный режим приближения к особой точке в релятивистской космологии

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СОДЕРЖАНИЕ
1. Введение
2. Обобщенное решение Казнера
3. Колебательный режим приближения к особой точке
4. Эволюция модели под влиянием двух возмущений
5. Эволюция модели в асимптотической области сколь угодно малых времен
6. Статистический анализ эволюции модели при приближении к особой точке
7. Построение общего решения для длинной эры с малыми колебаниями
8. Заключительные замечания
Приложения
A. Некоторые сведения из теории непрерывных дробей
Б. Уточнение расчетов к разделу 4
B. Однородные пространства
Г. Однородные пространства типов VII и IX
Цитированная литература

Текст pdf (2,5 Мб)
English fulltext is available at DOI: 10.1070/PU1971v013n06ABEH004279
PACS: 98.80.Jk, 04.20.Jb, 95.30.Sf (все)
DOI: 10.3367/UFNr.0102.197011d.0463
URL: https://ufn.ru/ru/articles/1970/11/d/
Цитата: Белинский В А, Лифшиц Е М, Халатников И М "Колебательный режим приближения к особой точке в релятивистской космологии" УФН 102 463–500 (1970)
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English citation: Belinskii V A, Lifshitz E M, Khalatnikov I M “Oscillatory approach to the singular point in relativistic cosmology” Sov. Phys. Usp. 13 745–765 (1971); DOI: 10.1070/PU1971v013n06ABEH004279

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  21. Byalko A V Biogr. Mems Fell. R. Soc. 72 251 (2022)
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  23. De Falco V, Borrelli W Phys. Rev. D 103 (6) (2021)
  24. Scott S M, Whale B E Class. Quantum Grav. 38 065012 (2021)
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  36. Calcagni G Classical and Quantum Cosmology Graduate Texts in Physics Chapter 6 (2017) p. 261
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  38. Garfinkle D Rep. Prog. Phys. 80 016901 (2017)
  39. Barrow J D, Ganguly Ch Phys. Rev. D 95 (8) (2017)
  40. Ali M, Husain V Phys. Rev. D 96 (4) (2017)
  41. Czuchry E, Garfinkle D et al Phys. Rev. D 95 (2) (2017)
  42. Chugreev Yu V Phys. Part. Nuclei Lett. 14 539 (2017)
  43. Saini S, Singh P Class. Quantum Grav. 34 235006 (2017)
  44. Ferronsky V I Gravitation, Inertia and Weightlessness Chapter 9 (2016) p. 281
  45. Ivashchuk V D Eur. Phys. J. C 76 (5) (2016)
  46. Popławski N ApJ 832 96 (2016)
  47. Cataldo M, Cid A et al 57 (11) (2016)
  48. Barceló C, Carballo-Rubio R, Garay L Universe 2 7 (2016)
  49. Ivashchuk V D, Melnikov V N Gravit. Cosmol. 22 166 (2016)
  50. Guo Ju-Q, Joshi P S Phys. Rev. D 92 (6) (2015)
  51. Khalatnikov I M, Kamenshchik A Yu Успехи физических наук 185 948 (2015)
  52. [Khalatnikov I M, Kamenshchik A Yu Phys.-Usp. 58 878 (2015)]
  53. Burlankov D E Gravit. Cosmol. 21 175 (2015)
  54. Rubakov V A Успехи физических наук 184 137 (2014)
  55. [Rubakov V A Phys.-Usp. 57 128 (2014)]
  56. Berger B K Springer Handbook of Spacetime Springer Handbooks Chapter 21 (2014) p. 437
  57. Scheel M A, Thorne K S Успехи физических наук 184 367 (2014)
  58. [Scheel M A, Thorne K S Phys.-Usp. 57 342 (2014)]
  59. Novello M, Bittencourt E, Salim J M Braz J Phys 44 832 (2014)
  60. Kohli I S, Haslam M C Phys. Rev. D 89 (4) (2014)
  61. Rennert Ju, Sloan D Class. Quantum Grav. 31 015017 (2014)
  62. LUKASH VLADIMIR N, STROKOV VLADIMIR N Int. J. Mod. Phys. A 28 1350007 (2013)
  63. Ivashchuk V D, Melnikov V N Gravit. Cosmol. 19 171 (2013)
  64. Kim E J, Kawai Sh Phys. Rev. D 87 (8) (2013)
  65. Lecian O M, Montani G, Moriconi R Phys. Rev. D 88 (10) (2013)
  66. Lecian O M Phys. Rev. D 88 (10) (2013)
  67. Ferronsky V I, Ferronsky S V Formation of the Solar System Chapter 10 (2013) p. 289
  68. Garfinkle D Class. Quantum Grav. 29 244003 (2012)
  69. Gaspar Y, Acquaviva G Eur. Phys. J. Plus 127 (6) (2012)
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  71. Ferronsky V I, Denisik S A, Ferronsky S V Astrophysics and Space Science Library Vol. Jacobi DynamicsConclusions369 Chapter 10 (2011) p. 311
  72. Penrose R Phil. Trans. R. Soc. A. 369 4864 (2011)
  73. MARCOLLI MATILDE Int. J. Geom. Methods Mod. Phys. 08 1131 (2011)
  74. Damour T, Lecian O M Phys. Rev. D 83 (4) (2011)
  75. Ferronsky V I, Denisik S A, Ferronsky S V Astrophysics and Space Science Library Vol. Jacobi DynamicsIntroduction: General Principles and Approaches in Dynamics369 Chapter 1 (2011) p. 1
  76. Middleton J Class. Quantum Grav. 27 225013 (2010)
  77. Abdolrahimi Sh, Shoom A A, Page D N Phys. Rev. D 82 (12) (2010)
  78. Ivashchuk V D Gravit. Cosmol. 16 118 (2010)
  79. Saotome R, Akhoury R, Garfinkle D Class. Quantum Grav. 27 165019 (2010)
  80. Kamenshchik A Yu Uspekhi Fizicheskikh Nauk 180 313 (2010)
  81. Penrose R J. Phys.: Conf. Ser. 174 012001 (2009)
  82. Saha B, Rikhvitsky V Phys. Part. Nuclei 40 612 (2009)
  83. Ivashchuk V D, Melnikov V N Gravit. Cosmol. 15 49 (2009)
  84. Choquet-Bruhat Y General Relativity and the Einstein Equations 1 (2008)
  85. Garfinkle D Class. Quantum Grav. 24 S295 (2007)
  86. GIOVANNINI MASSIMO Int. J. Mod. Phys. A 22 2697 (2007)
  87. Szydłowski M J. Cosmol. Astropart. Phys. 2007 007 (2007)
  88. Berger B K Lecture Notes in Physics Vol. Analytical and Numerical Approaches to Mathematical RelativityComputer Simulation – a Tool for Mathematical Relativity – and Vice Versa692 Chapter 9 (2006) p. 187
  89. Da̧browski M P Annalen der Physik 518 352 (2006)
  90. Clifton T, Barrow J D Class. Quantum Grav. 23 2951 (2006)
  91. Lidsey Ja E Class. Quantum Grav. 23 3517 (2006)
  92. Berger B K Gen Relativ Gravit 38 625 (2006)
  93. Polarski D Annalen der Physik 518 342 (2006)
  94. Barrow J D, Clifton T Class. Quantum Grav. 23 L1 (2006)
  95. Giovannini M Physics Letters B 634 1 (2006)
  96. Carr B J, Coley A A Gen Relativ Gravit 37 2165 (2005)
  97. Ivashchuk V D, Melnikov V N, Singleton D Phys. Rev. D 72 (10) (2005)
  98. Coley A A Can. J. Phys. 83 475 (2005)
  99. Novikov I D Springer Proceedings in Physics Vol. Particle Physics and the UniverseThe Internal Structure of Black Holes98 Chapter 10 (2005) p. 113
  100. Giovannini M J. Cosmol. Astropart. Phys. 2005 009 (2005)
  101. Curtis J, Garfinkle D Phys. Rev. D 72 (6) (2005)
  102. Garfinkle D Phys. Rev. Lett. 93 (16) (2004)
  103. Ivashchuk V D The Gravitational Constant: Generalized Gravitational Theories and Experiments Chapter 10 (2004) p. 205
  104. Berger B K Class. Quantum Grav. 21 S81 (2004)
  105. Horowitz G T, Maldacena Ju J. High Energy Phys. 2004 008 (2004)
  106. Harko T, Mak M K Class. Quantum Grav. 21 1489 (2004)
  107. GARFINKLE DAVID Int. J. Mod. Phys. D 13 2261 (2004)
  108. Ibáñez J, Jhingan S Phys. Rev. D 70 (6) (2004)
  109. Damour T International Conference on Theoretical Physics Chapter 23 (2003) p. 291
  110. Da̧browski M P, Stachowiak T, Szydłowski M Phys. Rev. D 68 (10) (2003)
  111. Novikov* I D Surveys in High Energy Physics 18 139 (2003)
  112. Garfinkle D Phys. Rev. D 65 (4) (2002)
  113. Coley A A Class. Quantum Grav. 19 L45 (2002)
  114. Cotsakis S Astrophysics and Space Science Library Vol. Modern Theoretical and Observational CosmologyCurrent Trends in Mathematical Cosmology276 Chapter 1 (2002) p. 5
  115. Berger B K Living Rev. Relativ. 5 (1) (2002)
  116. Garfinkle D Lecture Notes in Physics Vol. The Conformal Structure of Space-TimeSimulations of Generic Singularities in Harmonic Coordinates604 Chapter 18 (2002) p. 349
  117. Anninos P Living Rev. Relativ. 4 (1) (2001)
  118. Obregón O, Quevedo H, Ryan M P Phys. Rev. D 65 (2) (2001)
  119. Ivashchuk V D, Melnikov V N Class. Quantum Grav. 18 R87 (2001)
  120. Lehner L Class. Quantum Grav. 18 R25 (2001)
  121. Ruban V P, Podolsky D I Phys. Rev. D 64 (4) (2001)
  122. Dymnikova I G, Dobosz A et al Physics Letters B 506 351 (2001)
  123. Kunze K E, Durrer R Class. Quantum Grav. 17 2597 (2000)
  124. Berger B K, Moncrief V Phys. Rev. D 62 (12) (2000)
  125. Veneziano G Les Houches - Ecole d’Ete de Physique Theorique Vol. The primordial universe - L’univers primordialString Cosmology: The pre-Big Bang Scenario71 Chapter 12 (2000) p. 581
  126. Da̧browski M P Physics Letters B 474 52 (2000)
  127. Berger B K, Moncrief V Phys. Rev. D 62 (2) (2000)
  128. Gibbons G W, Rychenkova P Journal of Geometry and Physics 32 311 (2000)
  129. Ivashchuk V D, Melnikov V N 41 6341 (2000)
  130. Berger B K Phys. Rev. D 61 (2) (1999)
  131. Donets E E, Tentyukov M N, Tsulaia M M Phys. Rev. D 59 (6) (1999)
  132. Lazkoz R Phys. Rev. D 60 (10) (1999)
  133. Buonanno A, Damour T, Veneziano G Nuclear Physics B 543 275 (1999)
  134. Ori A Phys. Rev. Lett. 83 5423 (1999)
  135. Giovannini M Phys. Rev. D 59 (6) (1999)
  136. Cotsakis S, Lemmer R L, Leach P G L Phys. Rev. D 57 4691 (1998)
  137. Khalatnikov I M, Kamenshchik A Yu Успехи физических наук 168 593 (1998)
  138. Weaver M, Isenberg Ja, Berger B K Phys. Rev. Lett. 80 2984 (1998)
  139. Foster S Class. Quantum Grav. 15 3485 (1998)
  140. Berger B K Living Rev. Relativ. 1 (1) (1998)
  141. Gertsenshtein M E Russ Phys J 41 193 (1998)
  142. Anninos P Living Rev. Relativ. 1 (1) (1998)
  143. BERGER B K, GARFINKLE D et al Mod. Phys. Lett. A 13 1565 (1998)
  144. Berger B K, Moncrief V Phys. Rev. D 57 7235 (1998)
  145. Anninos P Living Rev. Relativ. 1 (1) (1998)
  146. Argyris J, Andreadis I, Ciubotariu C Chaos, Solitons & Fractals 9 1813 (1998)
  147. Berger B K, Garfinkle D Phys. Rev. D 57 4767 (1998)
  148. Berger B K, Moncrief V Phys. Rev. D 58 (6) (1998)
  149. Barrow J D, Da̧browski M P Phys. Rev. D 57 7204 (1998)
  150. Kasper U, Rainer M, Zhuk A General Relativity and Gravitation 29 1123 (1997)
  151. Khalatnikov I M, Kamenshchik A Yu Physics Reports 288 513 (1997)
  152. Demaret Ja, Scheen Ch J. Phys. A: Math. Gen. 29 59 (1996)
  153. Berger B K Class. Quantum Grav. 13 1273 (1996)
  154. Cheb-Terrab E S, de Oliveira H P Computer Physics Communications 95 171 (1996)
  155. Berger B K Relativity and Scientific Computing Chapter 8 (1996) p. 152
  156. Barrow J D Class. Quantum Grav. 13 2965 (1996)
  157. González G, Tate R S Class. Quantum Grav. 12 1287 (1995)
  158. Gavrilov V R, Ivashchuk V D, Melnikov V N 36 5829 (1995)
  159. Ivashchuk V D, Melnikov V N Lecture Notes in Physics Vol. Birth of the Universe and Fundamental PhysicsBilliard representation for multidimensional quantum cosmology near the singularity455 Chapter 21 (1995) p. 121
  160. Graham R Chaos, Solitons & Fractals 5 1103 (1995)
  161. Kirillov A A, Melnikov V N Phys. Rev. D 52 723 (1995)
  162. Sobolev A I, Kurbatov A M et al Encyclopaedia of Mathematics Chapter 1 (1995) p. 1
  163. Ivashchuk V D, Melnikov V N Class. Quantum Grav. 12 809 (1995)
  164. Skornyakov L A, Mysovskikh I P et al Encyclopaedia of Mathematics Chapter 6 (1995) p. 715
  165. Hobill D NATO ASI Series Vol. Deterministic Chaos in General RelativityA Brief Review of “Deterministic Chaos in General Relativity”332 Chapter 1 (1994) p. 1
  166. Berger B K NATO ASI Series Vol. Deterministic Chaos in General RelativityThe Belinskii-Khalatnikov-Lifshitz Discrete Evolution as an Approximation to Mixmaster Dynamics332 Chapter 19 (1994) p. 329
  167. Francisco G, Matsas G E A NATO ASI Series Vol. Deterministic Chaos in General RelativityThe Chaoticity of the Bianchi IX Cosmological Model332 Chapter 21 (1994) p. 355
  168. Berger B K Phys. Rev. D 49 1120 (1994)
  169. MacCallum M A H NATO ASI Series Vol. Deterministic Chaos in General RelativityRelativistic Cosmologies332 Chapter 11 (1994) p. 179
  170. Grubišić Boro, Moncrief V Phys. Rev. D 49 2792 (1994)
  171. Dettmann C P, Frankel N E, Cornish N J Phys. Rev. D 50 R618 (1994)
  172. Verdaguer E Physics Reports 229 1 (1993)
  173. Berger B K Phys. Rev. D 47 3222 (1993)
  174. Berger B K, Moncrief V Phys. Rev. D 48 4676 (1993)
  175. BELINSKII V A, LIFSHITZ E M et al Perspectives in Theoretical Physics (1992) p. 677
  176. Hazewinkel M Encyclopaedia of Mathematics Chapter 1 (1992) p. 1
  177. Khalatnikov I M Gravitation and Modern Cosmology Chapter 8 (1991) p. 65
  178. Parnovsky S L Class. Quantum Grav. 7 571 (1990)
  179. Particle Physics and Inflationary Cosmology (1990) p. 337
  180. Liddle A R, Moorhouse R G, Henriques A B Nuclear Physics B 311 719 (1989)
  181. Qadir A, Archibald W J Nuclear Physics B - Proceedings Supplements 6 345 (1989)
  182. Barrow J D The Early Universe Chapter 4 (1988) p. 125
  183. Hazewinkel M Encyclopaedia of Mathematics Chapter 1 (1988) p. 1
  184. Fuchs H, Kasper U et al Fortschr. Phys. 36 427 (1988)
  185. Barrow J D Lecture Notes in Physics Vol. The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner FunctionChaotic space-times278 Chapter 5 (1987) p. 18
  186. Henriques A B, Moorhouse R G Physics Letters B 194 353 (1987)
  187. Gertsenshtein M E, Melkumova E Yu Soviet Physics Journal 30 174 (1987)
  188. Barrow J D NATO ASI Series Vol. Gravitation in AstrophysicsSome Topics in Relativistic Cosmology156 Chapter 9 (1987) p. 239
  189. Barrow J D, Stein-Schabes J Physics Letters B 167 173 (1986)
  190. Ibanez J, Verdaguer E Class. Quantum Grav. 3 1235 (1986)
  191. Barrow J D, Sonoda D H Gen Relat Gravit 17 409 (1985)
  192. Thorne K S Springer Proceedings in Physics Vol. Nonlinear Phenomena in PhysicsThe Dynamics of Spacetime Curvature: Nonlinear Aspects3 Chapter 11 (1985) p. 280
  193. Barrow J D, Stein-Schabes J Phys. Rev. D 32 1595 (1985)
  194. Peresetskii A A Topics in Modern Mathematics Chapter 6 (1985) p. 173
  195. Hawking S W, Luttrell Ju C Physics Letters B 143 83 (1984)
  196. Sato H 72 98 (1984)
  197. Carmeli M, Charach Ch Found Phys 14 963 (1984)
  198. Zardecki A Phys. Rev. D 28 1235 (1983)
  199. Chernoff D F, Barrow J D Phys. Rev. Lett. 50 134 (1983)
  200. Carr B J, Verdaguer E Phys. Rev. D 28 2995 (1983)
  201. Bogoyavlenskii O I, Novikov S P J Math Sci 21 254 (1983)
  202. MacCallum M A H The Origin and Evolution of Galaxies Chapter 2 (1983) p. 9
  203. Barrow J D Physics Reports 85 1 (1982)
  204. Spokoiny B L Gen Relat Gravit 14 279 (1982)
  205. Obregón O, Ryan M P 22 623 (1981)
  206. Parnovsky S L Physica A: Statistical Mechanics and its Applications 104 210 (1980)
  207. Wheeler J A Essays in General Relativity (1980) p. 59
  208. Grigoryan S D Mathematical Notes of the Academy of Sciences of the USSR 26 610 (1979)
  209. Barrow J D, Tipler F J Physics Reports 56 371 (1979)
  210. MacCallum M Lecture Notes in Physics Vol. Physics of the Expanding UniverseThe mathematics of anisotropic spatially-homogeneous cosmologies109 Chapter 1 (1979) p. 1
  211. Gertsenshtein M E, Ingel’ L Kh, Fil’chenkov M L Soviet Physics Journal 21 841 (1978)
  212. Ginsburg W L Über Physik und Astrophysik Chapter 6 (1977) p. 139
  213. Misner Ch W Cosmology, History, and Theology Chapter 7 (1977) p. 75
  214. Christodoulou D, Francaviglia M Reports on Mathematical Physics 11 377 (1977)
  215. Bogoyavlenskii O I Theor Math Phys 27 414 (1976)
  216. Lukash V N, Novikov I D et al Nuov Cim B 35 293 (1976)
  217. Lukash V N Nuov Cim B 35 268 (1976)
  218. Goorjian P Phys. Rev. D 12 2978 (1975)
  219. Hu B L Phys. Rev. D 12 1551 (1975)
  220. Weinberg S Phys. Rev. D 9 3357 (1974)
  221. Eardley D M Commun.Math. Phys. 37 287 (1974)
  222. Hu B L Phys. Rev. D 9 3263 (1974)
  223. Misner Ch W Phys. Rev. D 8 3271 (1973)
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