ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Mukhin R. R. From the history of hamiltonian chaos: research of stochasticity in nonlinear systems by the novosibirsk school. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 5, pp. 67-82. DOI: 10.18500/0869-6632-2008-16-5-67-82

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Russian
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Personalia
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537

From the history of hamiltonian chaos: research of stochasticity in nonlinear systems by the novosibirsk school

Autors: 
Mukhin Ravil Rafkatovich, Stary Oskol technological Institute. A. A. Ugarov (branch) of Federal state educational institution of higher professional education "national research technological University "MISIS" (STI nust Misa)
Abstract: 

The article is devoted to the problems of history of the Hamiltonian chaos discovery in 1960th which is described a little in publications in comparison with the history of dissipative chaos. The main center of Hamiltonian chaos research was the Nuclear Physics Institute in Novosibirsk where B.V. Chirikov and G.M. Zaslavsky worked, being the major specialists in the world in this field of science.

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Reference: 
  1. Balakin VE, Barkov LM, Dikanskii NS, Dimov GI, Kruglyakov EP, Kulipanov GN, Meshkov IN, Parkhomchuk VV, Sidorov VA, Skrinskii AN. Boris Valerianovich Chirikov (on his seventieth birthday). Phys. Usp. 1998;41(7):731–732. DOI: 10.1070/PU1998v041n07ABEH000425.
  2. Chirikov BV. Life is creativity! In: Academician G. I. Budker: Essays, Memoirs. Novosibirsk: Nauka; 1988. P. 67–76 (in Russian).
  3. Sagdeev RZ. How much porridge was eaten. In: Academician M.A. Leontovich. Moscow: Nauka; 2003. P. 287–289 (in Russian).
  4. Kogan VI. Oral communication dated 17.12.2003 (in Russian).
  5. Vizgin VP. Oral communication dated 23.11.2004 (in Russian).
  6. Mukhin RR. «For understanding the structure and nature of rings, the old methods of celestial mechanics turned out to be inapplicable». Interview with A.M. Friedman. Questions on History of Natural Sciences and Technology. 2005;(3):157–168 (in Russian).
  7. Burshtein AI. Return of «Integral». In: Scientific Community of Physicists of the USSR. 1950s-1960s. Vol. 1. St. Petersburg: RCAH Publishing; 2005. P. 569–618 (in Russian).
  8. «Science in Siberia» – 28 June 1990. No. 23–24 (in Russian).
  9. Zaslavsky GM. Oral communication dated 25.08.2006 (in Russian).
  10. Budker GI. Thermonuclear reactions in a system with magnetic mirrors. In: Plasma Physics and the Problem of Controlled Reactions. Vol. 3. Moscow: AS USSR Publishing; 1958. P. 3–31 (in Russian).
  11. Zaslavskii GM, Chirikov BV. Stochastic instability of non-linear oscillations. Sov. Phys. Usp. 1972;14(5):549–568. DOI: 10.1070/PU1972v014n05ABEH004669.
  12. Chirikov BV. Written message dated 11.17.2003 (in Russian).
  13. Sinai YG. How mathematicians and physicists found each other. In: Mathematical Events of the 20th Century. Moscow: Fazis; 2003. P. 417–426 (in Russian).
  14. Chirikov BV. Research on the theory of nonlinear resonance and stochasticity. Preprint Budker Institute of Nuclear Physics of USSR Academy of Sciences. No. 267. Novosibirsk: Budker Institute of Nuclear Physics of USSR Academy of Sciences; 1969 (in Russian).
  15. Izrailev FM. Oral communication dated 2.07.2004 (in Russian).
  16. Chirikov BV. Resonant processes in magnetic traps. Atomic Energy. 1959;6(6):630–638 (in Russian).
  17. Zaslavsky GM, Chirikov BV. On the mechanism of Fermi acceleration in the one-dimensional case. Proc. Acad. Sci. USSR. 1964;159(2):306–309 (in Russian).
  18. Andronov AA, Leontovich MA, Mandel'shtam LI. On the theory of adiabatic invariants. Journal of the Russian Physicochemical Society. 1928:60(1):413–419 (in Russian).
  19. Chirikov BV. A universal instability of many-dimensional oscillator systems. Phys. Rep. 1979;52(5):263–379. DOI: 10.1016/0370-1573(79)90023-1.
  20. Rosenbluth MN, Sagdeev RZ, Taylor JB, Zaslavsky GM. Destruction of magnetic surfaces by magnetic field irregularities. Nucl. Fusion. 1966;6(4):297–300. DOI: 10.1088/0029-5515/6/4/008.
  21. Filonenko NN, Sagdeev RZ, Zaslavsky GM. Destruction of magnetic surfaces by magnetic field irregularities. Part II. Nucl. Fusion. 1967;7(4):253–266. DOI: 10.1088/0029-5515/7/4/009.
  22. Zaslavsky GM, Filonenko NN. Stochastic instability of trapped particles and conditions for the applicability of the quasilinear approximation. Sov. Phys. JETP. 1968;54(5):1590–1602 (in Russian).
  23. Zaslavsky GM. Written message dated 02.12.2003 (in Russian).
  24. Zaslavsky GM. Statistical Irreversibility in Nonlinear Systems. Moscow: Nauka; 1970. 144 p. (in Russian).
  25. Zubarev DN. Modern methods of the statistical theory of nonequilibrium processes. J Math. Sci. 1981;16(6):1509–1571. DOI: 10.1007/BF01091712.
  26. Kac M. Probability and Related Topics in Physical Sciences. Amer Mathematical Society; 1957. 266 p.
  27. Prigogine I. Non-equilibrium Statistical Mechanics. Interscience Publishers; 1962. 319 p.
  28. Fermi E, Pasta J, Ulam S. Studies of nonlinear problems. In: Studies of Nonlinear Problems. I. Report LA-1940. Los Alamos Scientific Laboratory of the University of California; 1955. 21 p.
  29. Fermi E. Beweis dass ein Mechnisches Normalsystem in Allgemeinen Quasi-ergodisch ist. Phys. Zs. 1923;24:261–265 (in German).
  30. Campbell DK. Introduction: The Fermi–Pasta–Ulam problem—The first fifty years. Chaos. 2005;15(1):015101. DOI: 10.1063/1.1889345.
  31. Zabusky NJ, Kruskal MD. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 1965;15(6):240–243. DOI: 10.1103/PhysRevLett.15.240.
  32. Gardner CS, Green JM, Kruskal MD, Miura KM. Method for the solving the Korteweg – deVries equation. Phys. Rev. Lett. 1967;19(19):1095–1097. DOI: 10.1103/PhysRevLett.19.1095.
  33. Bullough RK, Caudrey PJ. Solitons. Berlin: Springer; 1980. 392 p. DOI: 10.1007/978-3-642-81448-8.
  34. Ulam S. John von Neumann (1903–1957). Bull. Amer. Math. Soc. 1958;64(3):1–49.
  35. Berks A. Introduction to the book: J. von Neumann. The Theory of Self-Replicating Automata. Moscow: Mir; 1971. P. 20 (in Russian).
  36. Zaslavsky GM. Written message dated 04.03.2004 (in Russian).
  37. Fermi E. On the origin of cosmic radiation. Phys. Rev. 1949;75(8):1169–1174. DOI: 10.1103/PhysRev.75.1169.
  38. Ulam S. On some statistical properties of dynamical systems. In: Proc. 4-th Berkeley Symposium on Mathematical Statistics and Probability. Vol. 3. Berkeley, Los Angeles; 1961. P. 315–320.
  39. Zaslavsky GM. Long way from FPU-problem to chaos. Chaos. 2005;15(1):015103. DOI: 10.1063/1.1858115.
  40. Lichtenberg AJ, Lieberman MA. Regular and Stochastic Dynamics. New York: Springer; 1992. 692 p. DOI: 10.1007/978-1-4757-2184-3.
  41. Izrailev FM, Chirikov BV. Statistical properties of a nonlinear string. Proc. Acad. Sci. USSR. 1966;166(1):57–59 (in Russian).
  42. Izrailev FM, Khisamutdinov AI, Chirikov BV. Numerical Experiments With A Nonlinear Chain. Budker Institute of Nuclear Physics of USSR Academy of Sciences. No. 252. Novosibirsk: Budker Institute of Nuclear Physics of USSR Academy of Sciences; 1968. 36 p. (in Russian).
  43. Izrailev FM, Chirikov BV. Stochasticity of the simplest dynamic model with a split phase space. Budker Institute of Nuclear Physics of USSR Academy of Sciences. No. 191. Novosibirsk: Budker Institute of Nuclear Physics of USSR Academy of Sciences; 1968. 64 p. (in Russian).
  44. Ruelle D, Takens F. On the nature of turbulence. Commun. Math. Phys. 1971;20(3):167–192. DOI: 10.1007/BF01646553.
  45. Lorenz E. Deterministic nonperiodic flow. J. Atmosph. Sci. 1963;20(2):130–141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
Received: 
21.02.2008
Accepted: 
17.04.2008
Published: 
31.12.2008
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