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Publications: 1. Classical Chaos

(Summer forest, Akademgorodok)

1981
1.1. B.V.Chirikov, F.M.Izrailev, D.L.Shepelyansky, "Dynamical Stochasticity in Classical and Quantum Mechanics", Sov. Scient. Rev. v.2C, p.209-267 (1981) [Section C - Mathematical Physics Reviews, Ed. S.P.Novikov vol.2, Harwood Acad. Publ., Chur, Switzerland (1981)] (here) ; [Preprint INP 80-209, Novosibirsk 1980, BINP copy in Russian (here) ; Preprint INP 80-210, dated 11 November 1980, BINP copy in English (here) ]
1.2. B.V.Chirikov, 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) BINP copy (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 v.2, p.420-425 (1984) (in Russian (here) )
1.3. B.V.Chirikov, J.Ford, F.M.Izrailev, D.L.Shepelyansky, F.Vivaldi, "Modulational Diffusion in Nonlinear Oscillating Systems", Proc. IX Int. Conf. on Nonlinear Oscillations (Kiev 1981), Naukova Dumka v.2, p.80-85 (1984) (in Russian (here); BINP copy (here))
1.4. B.V.Chirikov, D.L.Shepelyansky, "Stochastic Oscillations of Classical Yang-Mills Fields", Pis'ma Zh. Eksp. Teor. Fiz. v.34, p.171-175 (1981) (in Russian: scan (here) and JETPLett-copy (here) )
1982
1.5. B.V.Chirikov, D.L.Shepelyansky, "Dynamics of Some Homogeneous Models of Classical Yang-Mills Fields", Yader. Fiz. v.36, p.1563-1576 (1982) (in Russian (here) ); [B.V.Chirikov and D.L.Shepelyanskii, Sov. J.Nucl. Phys. v.36(6), p.908 (1982), in English (here) ]; [B.V.Chirikov and D.L.Shepelyanskii, JETP Lett., v.34, p.163-166 (1981), in English (here) ]; [Preprint INP 82-120, Novosibirsk 1982, BINP copy in Russian (here) ]
1.6. B.V.Chirikov, D.L.Shepelyansky, "Diffusion for Multiple Crossing of Nonlinear Resonance", Zh. Tech. Fiz. v.52, p.238-245 (1982) (in Russian (here) ); [B.V.Chirikov, D.L.Shepelyanskii, Sov. Phys. Tech. Phys. v.27(2), p.156-160 (1982), in English (here) ]; [Preprint INP 80-211, Novosibirsk 1980, BINP copy in Russian (here) ]
1984
1.7. B.V.Chirikov, 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) ; BINP copy (here) )
1985
1.8. B.V.Chirikov, M.A.Lieberman, D.L.Shepelyansky, F.Vivaldi, "A Theory of Modulational Diffusion", Physica v.14D, p.289-304 (1985) (here)
1986
1.9. D.L.Shepelyansky, "Chaos and Interaction of Atoms with Self-Consistent Field in the Case of Small Coupling Constant", Phys. Rev. Lett. v.57, p.1815-1818 (1986) (here)
1988
1.10. B.V.Chirikov, 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) ; Preprint INP 86-174, Novosibirsk 26 June 1986, BINP copy in Russian (here)
1.11. B.V.Chirikov, D.L.Shepelyansky, "Renormalization Chaos and Motion Statistical Properties", Phys. Rev. Lett. v.61, p.1039-1039 (1988) (here)
1991
1.12. R.Artuso, G.Casati, D.L.Shepelyansky, "Breakdown of Universality in Renormalization Dynamics for Critical Invariant Torus" Europhys. Lett., v.15 N4, p.381-386 (1991) (here)
1992
1.13. R.Artuso, G.Casati, D.L.Shepelyansky, "Breakup of the Spiral Mean Torus in a Volume-preserving Map", Chaos, Solitons & Fractals, v.2, N2 (1992) p.181-190 (here)
1996
1.14. S.Ruffo, D.L.Shepelyansky, "Universal diffusion near the golden chaos border", Phys. Rev. Lett. v.76 (1996) p.3300-3303 (here)
1997
1.15. D.L.Shepelyansky, "Low energy chaos in the Fermi-Pasta-Ulam problem", Nonlinearity, v.10 (1997) p.1331-1338 (chao-dyn/9611005) (here)
1999
1.16. B.V.Chirikov and D.L.Shepelyansky, "Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space", Phys. Rev. Lett. v.82 (1999) p.528 - 531 (cond-mat/9807365) (here) ; Preprint BINP 98-63, Novosibirsk 26 August 1998, BINP copy in English (here) ; [also ``To the problem of Poincar\'e recurrences in generic Hamiltonian systems'' (cond-mat/0207705) and Phys. Rev. Lett. v.89 (2002) p.239402 (here) ].
2009
1.17. D.L.Shepelyansky and O.V.Zhirov, "Google matrix and dynamical attractors", (arxiv:0905.4162[cs.IR] (here) ); revised version Phys. Rev. E v.81, p.036213 (2010) "Google matrix, dynamical attractors and Ulam networks" (here) (arxiv:0905.4162v2[cs.IR] (here) )
1.18. I.B.Khriplovich and D.L.Shepelyansky, "Capture of dark matter by the Solar System", International Journal of Modern Physics D (IJMPD) v.18(12), pp.1903-1912 (2009) (DOI: 10.1142/S0218271809015758 for private use only) (here) (arxiv:0906.2480[astro-ph] (here) )
1.19. L.Ermann and D.L.Shepelyansky, "Google matrix and Ulam networks of intermittency maps", Phys. Rev E v.81, p.036221 (2010) (here) (arxiv:0911.3823[cs.IR] (here) )

1.20. L.Ermann and D.L.Shepelyansky, "Ulam method and fractal Weyl law for Perron-Frobenius operators", Eur. Phys. J. B v.75, p.299-304 (2010) (here) (arxiv:0912.5083[nlin.CD] (here) )

2010
1.21. K.M.Frahm and D.L.Shepelyansky, "Ulam method for the Chirikov standard map", Eur. Phys. J. B v.76, p.57-68 (2010) (here) (arxiv:1004.1349[nlin.CD] (here) )
1.22. D.L.Shepelyansky, "Poincare recurrences in Hamiltonian systems with a few degrees of freedom", Phys. Rev. E v.82, p.055202(R) (2010) (here) (arxiv:1008.1465[nlin.CD] (here) ; update arxiv:1008.1465v2 (here) )
2011
1.23. M.Mulansky, K.Ahnert, A.Pikovsky and D.L.Shepelyansky, "Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems", J. Stat. Phys. v.145, p.1256-1274 (2011) (here) (arXiv:1103.2634v1 [nlin.CD] (here) )
1.23. L.Ermann and D.L.Shepelyansky, "The Arnold cat map, the Ulam method and time reversal", Physica D v.241, p.514 (2012) (here) (arxiv:1107.0437[nlin.CD] (here) )
1.24. K.M.Frahm and D.L.Shepelyansky, "Poincare recurrences of DNA sequences", Phys. Rev. E v.85, p.016214 (2012) (here) (arxiv:1109.0436[q-bio.GN] (here) ; update (here) ; update (here) )
2012
1.25 D.L.Shepelyansky, "Kolmogorov turbulence, Anderson localization and KAM integrability", Eur. Phys. J. B v.85, p.199 (2012) (here) (arXiv:1203.1130v1 [nlin.CD] (here) )
1.26. J.Lages and D.L.Shepelyansky, "Dark matter chaos in the Solar System", submitted 5 Nov 2012 (arXiv:1211.0903[astro-ph.EP] (here) )
2013
1.27. K.M.Frahm and D.L.Shepelyansky, "Poincare recurrences and Ulam method for the Chirikov standard map ", Eur. Phys. J. B v.86, p.322 (2013) (submitted EPJB 12 Feb 2013) (here) (arXiv:1302.2761 [nlin.CD] (here) )
2015
1.28. A.K.Mazur and D.L.Shepelyansky, "Algebraic statistics of Poincare recurrences in a DNA molecule", Phys. Rev. Lett. v.115, p.188104 (2015) (here) (arXiv:1508.01911 [q-bio.BM] (here) )
2016
1.29. D.L.Shepelyansky, "Chaotic delocalization of two interacting particles in the classical Harper model", Eur. Phys. J. B v.89, p.157 (2016) (here) (arXiv:1604.03291 [cond-mat.quant-gas] (here) )
2018
1.30. K.M.Frahm and D.L.Shepelyansky, "Small world of Ulam networks for chaotic Hamiltonian systems", Phys. Rev. E v.98, p.032205 (2018) (here) (arXiv:1807.05204 [nlin.CD] (here) )
1.31 L.Ermann and D.L.Shepelyansky, "Incommensurate standard map", Phys. Rev. E v.99, p.012215 (2019) (here) (arXiv:1810.11132 [nlin.CD] (here) )
2023
1.32. K.M.Frahm and D.L.Shepelyansky, "Goal quest for an intelligent surfer moving in a chaotic flow", Phys. Rev. E v.108, 054212 (2023) (here) ; (arXiv:2307.00019 [physics.soc-ph] (here) )