Back to home page

Publications of Boris Chirikov on Classical Chaos

(N.Roerich, 1936, Star of the Hero, Museum New York)

1959
1. B.V.Chirikov, "Resonance processes in magnetic traps", At. Energ. 6: 630 (1959) (in Russian - (here) ; better scan (here) ) [English translation: J. Nucl. Energy Part C: Plasma Phys. 1: 253 (1960) (in English (here) )]
2. B.V.Chirikov, "Resonance crossing for a nonlinear oscillator system", Doklady Acad. Nauk SSSR 1959: 1015 (1959) (in Russian - (here) )
1964
3. B.V.Chirikov and G.M.Zaslavsky, "On the mechanism of one-dimensional Fermi acceleration", Dokl. Akad. Nauk SSSR 159: 306 (1964) [in Russian (here) )]
1966
4. B.V.Chirikov and F.M.Izrailev, "Statistical properties of a non-linear string", Dokl. Akad. Nauk SSSR 166: 57 (1966) [English translation: (here) )]
1967
5. B.V.Chirikov, "Stochastic destruction of magnetic surfaces in stellarators", Dokl. Akad. Nauk SSSR 174: 1313 (1967) [in Russian (here) )]
1968
6. M.B.Antipov, F.M.Izrailev and B.V.Chirikov, "Statistical check of a generator of pseudo-random numbers", Vychislitelnie Systemy 30: 77 (1968) [in Russian (here) )]
1969
7. B.V.Chirikov, "Research concerning the theory of nonlinear resonance and stochasticity", Preprint N 267, Institute of Nuclear Physics, Novosibirsk (1969) (in Russian (here) ) [Engl. Transl., CERN Trans. 71 - 40, Geneva, October (1971), Translated by A.T.Sanders (here 48Mgb) ; (here part1 24Mgb) ; (here part2 24Mgb) ; good scan from CERN (here 12Mgb) ]
1971
8. B.V.Chirikov and G.M.Zaslavsky, "Stochastic instability of nonlinear oscillations", Uspekhi Fiz. Nauk 105: 3 (1971) (in Russian (here) ) [English translation: Sov. Phys. Uspekhi-USSR 14: 549 (1972) (to appear) )]
9. B.V.Chirikov, E.Keil and A.M.Sessler, "Stochasticity in many-dimensional nonlinear oscillating systems", J. Stat. Phys. 3(3): 307 (1971) (here) )]
1973
10. B.V.Chirikov, F.M.Izrailev, and V.A.Tayurski, "Numerical experiments on statistical behavior of dynamical systems with a few degrees of freedoms", Computer Phys. Comm. 5: 11 (1973) (here)
11. B.V.Chirikov and F.M.Izraelev, "Some numerical experiments with a nonlinear mapping: stochastic component", Proc. Colloques Internationaux du CNRS, Toulouse, N229, p. 409 (1973) (here) (better scan (here) )
1974
12. F.M.Izraelev and B.V.Chirikov, "Some numerical experiments with a simple model of turbulence", Meeting on Programming and mathematical Methods for Solving the Physical Problems, Dunba, Oct 30 - Nov4, 1973, Publ. Dubna (1974) p.266 (in Russian (here) )
1977
13. G.V.Gadiyak, F.M.Izrailev, and B.V.Chirikov, "Numerical experiments on universal instability in nonlinear oscillator systems", VII Internationale Konferenz uber nichtlineare Schwingungen, Band II, 1 Abbabdlungen der Akademie der Wissenschften der DDR, Abteilung Mathematik - Naturwissenschaften- Technik, Jahrgang 1977, Nr. 5 N, p.315, Akademie-Verlag-Berlin (1977) (in Russian (here) ; all front pages but not good copy (here) )
1978
14. B.V.Chirikov, "Stability of the motion of a charged particle in a magnetic confinement system", Sov. J.Plasma Phys. 4(3): 289 (1978) (here)
1979
15. B.V.Chirikov, "A universal instability of many-dimensional oscillator systems", Phys. Rep. 52: 263 (1979) (link here) ; see corrected missprints pages (here) ; (dve knigi NGU po russki: (part1 here) dli angliiskoi versii tozhe imia s e vmesto r; (part2 here) )
16. B.V.Chirikov, "Marginal local instability of quasi-periodic motion", Fizika Plasmy (Physics of Plasma) 5(4): 880 (1979) (in Russian (here) )
1980
17. G.Casati, B.V.Chirikov, and J.Ford, "Marginal local instability of quasi-periodic motion", Phys. Lett. A 77: 91 (1980) (here)
18. B.V.Chirikov, J.Ford and F.Vivaldi, "Some numerical studies of Arnold diffusion in a simple model", AIP Conf. Proc., January 1980, 57: 323 (1980) (DOI:10.1063/1.32115) (here)
1981
19. B.V.Chirikov, F.M.Izrailev and D.L.Shepelyansky, "Dynamical stochasticity in classical and quantum mechanics", Sov. Scient. Rev. C 2: 209 (1981) [Section C - Mathematical Physics Reviews, Ed. S.P.Novikov vol.2, Harwood Acad. Publ., Chur, Switzerland (1981)] (here)
20. B.V.Chirikov and D.L.Shepelyansky, "Statistics of Poincare Recurrences and the Structure of the Stochastic Layer of a Nonlinear Resonance", Dated: April 14, 1981, Preprint INP 81-69, Novosibirsk 1981 (in Russian (here) );
English translation available as Preprint PPPL-TRANS-133, Plasma Phys. Lab., Princeton Univ, Princeton, New Jersey, 1983 (here) ;
Proc. IX Int. Conf. on Nonlinear Oscillations (Kiev 1981), Naukova Dumka 2: 420 (1984) (in Russian (here) , better scan (here) )
21. F.Vivaldi, J.Ford, F.M.Izrailev, B.V.Chirikov and D.L.Shepelyansky, "Modulational diffusion in nonlinear oscillator systems", Proc. IX Int. Conf. on Nonlinear Oscillations (Kiev 1981), Naukova Dumka 2: 80 (1984) (in Russian (here) )
22. B.V.Chirikov and D.L.Shepelyansky, "Stochastic Oscillations of Classical Yang-Mills Fields", Pis'ma Zh. Eksp. Teor. Fiz. 34: 171 (1981) (in Russian: (here) ); [B.V.Chirikov and D.L.Shepelyanskii, JETP Lett., 34: 163 (1981), in English (here) ]
23. B.V.Chirikov and F.M.Izraelev, "Degeneration of turbulence in simple systems", Physica D 2: 30 (1981) (here)
1982
24. B.V.Chirikov and D.L.Shepelyansky, "Diffusion for multiple crossing of nonlinear resonance", Zh. Tech. Fiz. 52: 238-245 (1982) (in Russian (here) ) [B.V.Chirikov, D.L.Shepelyanskii, Sov. Phys. Tech. Phys. 27(2): 156-160 (1982), in English (here) ]
25. B.V.Chirikov and D.L.Shepelyansky, "Dynamics of some homogeneous nodels of classical Yang-Mills fields", Yader. Fiz. 36: 1563-1576 (1982) (in Russian (here) ) [B.V.Chirikov, D.L.Shepelyanskii, Sov. J.Nucl. Fiz. 36: 908 (1982), in English (here) ]
26. B.V.Chirikov, "The Nature and properties of dynamical chaos", p.553, Proc. 2nd Intern. Seminar on Group Theory Methods in Physics, Zvenigorod, (1982) (here)
1983
27. B.V.Chirikov, "Chaotic dynamics in Hamiltonian systems with divided phase space", Lecture Notes Phys. (Springer, Berlin) 179: 29 (1983) (DOI: 10.1007/3-540-12276-1) (here)
1984
28. B.V.Chirikov and D.L.Shepelyansky, "Correlation Properties of Dynamical Chaos in Hamiltonian Systems", Physica v.13D, p.395-400 (1984) (here) (in Russian preprint INP 83-149 (1983) (here) )
1985
29. B.V.Chirikov, M.A.Lieberman, D.L.Shepelyansky and F.Vivaldi, "A theory of modulational diffusion", Physica D 14: 289 (1985) (here)
1986
30. B.V.Chirikov, "Stability of particle motion in a magnetic trap", Fiz. Plasmy 12(5): 605 (1985), in Russian (here)
1987
31. B.V.Chirikov, "Particle confinement and adiabatic invariance", Proc. Royal Soc. London A 413: 145 (1987) (here)
32. B.V.Chirikov, "Particle dynamics in magnetic traps", Reviews of Plasma Physics, Ed. Acad. B.B.Kadomtsev, Vol. 13, p.1 - 92 (1987), Consultants Bureau, Plenum, New York, Translated from Russian by J.G.Adashko (here) (published in Russian in 1984 (here) )
1988
33. B.V.Chirikov and D.L.Shepelyansky, "Chaos border and statistical anomalies", Eds. D.V.Shirkov, D.I.Kazakov and A.A.Vladimirov, World Sci. Publ., Singapore, "Renormalization Group" p.221-250 (1988) (here)
34. B.V.Chirikov and D.L.Shepelyansky, "Renormalization chaos and motion statistical properties", Phys. Rev. Lett. 61: 1039 (1988) (here)
35. B.V.Chirikov, "Dynamical mechanisms of noise", p.415 in IV Int. Symposium on Selected Topics in Statistical Mechanics, D17-88-95, Dubna Aug 25-29 (1987), Publ. Dunbna (1988) (in Russian) (here)
36. B.V.Chirikov, "Asymptotic methods in adiamatic problems", p.277 in "Asymptotic methods of mathematical physics", Kiev, Naukova Dumka, (1988) (in Russian) (here)
1989
37. B.V.Chirikov and V.V.Vecheslavov, "Chaotic dynamics of comet Halley", Astron. Astrophys. 221: 146 (1989) (here) (in Russian Pisma Ast. Zhurn. 14(4):357 (1988) (here) )
1990
38. B.V.Chirikov and V.V.Vecheslavov, "KAM integrability", in "Analysis, et cetera" Eds. P.H.Rabinowitz and E.Zehnder, Research papers published in honor of Jurgen Moser's 60th birthday, Academic Press, Inc., N.Y. p.219 (1990) (here) (also Preprint INP 88-110, Novosibirsk (1988) (here), see also related Preprint INP 89-72, Novosibirsk (1989) (here) )
1991
39. B.V.Chirikov, "Patterns in chaos", Chaos, Solitons & Fractals 1(1): 79-103 (1991) (here) (Conf. Proc. (here) )
1992
40. B.V.Chirikov and V.V.Vecheslavov, "The structure of a weakly nonlinear resonance", in "From Phase Thansitions to Chaos: Topic in Modern Statistical Physics", G.Gyorgyi, I.Kondor, L.Sasvari and T.Tel (Eds.), World Scientific, Singapore (1992), pp. 273-289 (here)
1993
41. B.V.Chirikov and V.V.Vecheslavov, "Theory of fast Arnold diffusion in many-frequency systems", J. Stat. Phys. 71(1/2): 243 (1993) (here)
42. B.V.Chirikov, "Budker's problem of particle confinement and what has come about of it", p.157 in "Open plasma confinement systems for fusion" A.A.Kabantsev (Ed.), Int. Conference, Novosibirsk, Russia, June 14-18, World Sci., Singapore (1993) (here)
1995
43. G.Casati and B.V.Chirikov, "Comment on "Decoherence, chaos and the second law"", Phys. Rev. Lett. 75: 350 (1995) (here)
1996
44. B.V.Chirikov, "Anomalous diffusion in microtron and the critical structure on the chaos border", Zh. Eksp. Teor. Fiz. 110: 1174-1185 (1996) (in Russian ISSN: 0044-4510 (here) ) (English version (here) ; also available as preprint BINP 96-34, Novosibirsk 1996 (here) )
1997
45. B.V.Chirikov and V.V.Vecheslavov, "Arnold diffusion in large systems", Zh. Eksp. Teor. Fiz. 112: 1132-1146 (1997) [JETP 85(3): 616 (1997)] (here)
46. B.V.Chirikov, "Linear and nonlinear dynamical chaos", Open Sys. & Information Dyn. 4(3): 241-280 (1997) Kluwer Acad. Publ. (here) and (here)
47. B.V.Chirikov, "Pseudochaos in statistical physics", arXiv:chao-dyn/9705004 (1997), talk given at the Int. Conf. "Nonlinear Dynamics, Chaotic and Complex Systems", Zakopane (1995) (here) (Eds. E. Infeld, R. Zelazny, A. Galkowski, "Nonlinear Dynamics, Chaotic and Complex Systems", Cambridge Univ. Press p.149 (1997), (here) )
1998
48. V.V.Vecheslavov and B.V.Chirikov, "High-precision measurement of separatrix splitting in a nonlinear resonance", Zh. Eksp. Teor. Fiz. 114: 1516-1531 (1998) [JETP 87(4): 823 (1998)] (here)
1999
49. B.V.Chirikov and F.Vivaldi, "An algorithmic view of pseudochaos" Physica D 129: 223 (1999) (here)
50. B.V.Chirikov and D.L.Shepelyansky, "Asymptotic statistics of Poincare recurrences in Hamiltonian systems with divided phase space" Phys. Rev. Lett. 82: 528 (1999) (here) ; Phys. Rev. Lett. 89: 239402 (2002) (here)
2000
51. B.V.Chirikov and V.V.Vecheslavov, "Adiabatic invariance and separatrix: single separatrix crossing", Zh. Eksp. Teor. Fiz. 117(3): 644-652 (2000) [JETP 90(3): 562-569 (2000)] (here)
52. B.V.Chirikov and V.V.Vecheslavov, "Multiple separatrix crossing: a chaos structure", Zh. Eksp. Teor. Fiz. 117(5): 1030-1038 (2000) [JETP 90(5): 897-904 (2000)] (here)
53. G.Casati, B.V.Chirikov and O.V.Zhirov, "How many "arrows of time" do we really need to comprehend statistical laws?", Phys. Rev. Lett. 85: 896 (2000) (here)
54. B.V.Chirikov, "Poincare recurrences in microtron and the global critical structure", arXiv:nlin/0006013[nlin.CD] (2000) (here)
55. B.V.Chirikov and V.G.Davidovsky, "Dynamics of a simple model for turbulence of the second sound in helium II", arXiv:nlin/0006018[nlin.CD] (2000) (here)
56. B.V.Chirikov and V.G.Davidovsky, "Few-freedom turbulence", arXiv:nlin/0006020[nlin.CD] (2000) (here)
57. B.V.Chirikov, "Critical perturbation in standard map: a better approximation", arXiv:nlin/0006021[nlin.CD] (2000) (here)
2001
58. B.V.Chirikov, "Big entropy fluctuations in the nonequilibrium steady state: a simple model with the Gauss heat bath", Zh. Eksp. Teor. Fiz. 119(1): 205-220 (2001) [JETP 92(1): 179-193 (2001)] (here)
59. B.V.Chirikov and O.V.Zhirov, "Big entropy fluctuations in statistical equilibrium:: the macroscopic kinetics", Zh. Eksp. Teor. Fiz. 120(1): 214-223 (2001) [JETP 93(1): 188-196 (2001)] (here) (also B.V.Chirikov and O.V.Zhirov, "On the fluctuation law(s) for Hamiltonian systems (with equilibrium steady state): a comment on cond-mat/0008421" (2000) (here) )
60. V.V.Vecheslavov and B.V.Chirikov, "Separatrix conservation mechanism for nonlinear resonance in strong chaos", Zh. Eksp. Teor. Fiz. 120(3): 740-748 (2001) [JETP 93(3): 649-656 (2001)] (here) (in Russian (here) )
2002
61. V.V.Vecheslavov and B.V.Chirikov, "Diffusion in smooth Hamiltonian systems", Zh. Eksp. Teor. Fiz. 122(1): 175-187 (2002) [JETP 95(1): 154-165 (2002)] (here) (in Russian (here) )
62. B.V.Chirikov and V.V.Vecheslavov, " Fractal diffusion in smooth dynamical systems with virtual invariant curves", Zh. Eksp. Teor. Fiz. 122(3): 647-659 (2002) [JETP 95(3): 560-571 (2002)] (here)
63. B.V.Chirikov and D.L.Shepelyansky, "To the problem of Poincare recurrences in generic Hamiltonian systems", arXiv:/cond-mat/0207705 (2002) (here) (Chirikov and Shepelyansky Reply, Phys. Rev. Lett. Phys. Rev. Lett. 89: 239402 (2002) (here) )
2008
64. B.Chirikov and D.Shepelyansky, "Chirikov standard map" (invited article to Scholarpedia), Scholarpedia 3(3):3550 (2008) (here) ; (link)