Abstract.
We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about the first stage of this crossover phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.
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References
E. Ott, Chaos in dynamical system (Cambridge University Press, 1993)
Ya. Pesin, Russ. Math. Surveys 32, 55 (1977); Ya. Pesin in Hamiltonian Dynamical Systems: A Reprint Selection, edited by R.S. MacKay, J.D. Meiss (Adam Hilger, Bristol, 1987)
A.N. Kolmogorov, Dok. Acad. Nauk SSSR 119, 861 (1958); Ya.G. Sinai, Dok. Acad. Nauk SSSR 124, 768 (1959)
Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann, C. Tsallis (Oxford University Press, New York, 2004)
C. Tsallis, A.R. Plastino, W.-M. Zheng, Chaos, Solitons and Fractals 8, 885 (1997)
U.M.S. Costa, M.L. Lyra, A.R. Plastino, C. Tsallis, Phys. Rev. E 56, 245 (1997)
M.L. Lyra, C. Tsallis, Phys. Rev. Lett. 80, 53 (1998)
V. Latora, M. Baranger, A. Rapisarda, C. Tsallis, Phys. Lett. A 273, 97 (2000)
U. Tirnakli, G.F.J. Añaños, C. Tsallis, Phys. Lett. A 289, 51 (2001)
E.P. Borges, C. Tsallis, G.F.J. Añaños, P.M.C. de Oliveira, Phys. Rev. Lett. 89, 25 (2002)
F. Baldovin, A. Robledo, Europhys. Lett. 60, 518 (2002); F. Baldovin, A. Robledo, Phys. Rev. E 66, 045104(R) (2002)
F. Baldovin, A. Robledo, Phys. Rev. E 69, 045202(R) (2004)
C. Tsallis, J. Stat. Phys. 52, 479 (1988); for a recent review see C. Tsallis, in Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann, C. Tsallis (Oxford University Press, New York, 2004); for full bibliography see http://tsallis.cat.cbpf.br/biblio.htm
P. Grassberger, M. Scheunert, J. Stat. Phys. 26, 697 (1981); T. Schneider, A. Politi, D. Wurtz, Z. Phys. B 66, 469 (1987); G. Anania, A. Politi, Europhys. Lett. 7, 119 (1988); T. Horita, H. Hata, H. Mori, K. Tomita, Progr. Theor. Phys. 82, 897 (1989)
G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak chaos and quasi-regular patterns (Cambridge University Press)
G.M. Zaslavsky, Phys. Rep. 371, 461 (2002)
V.I. Arnold, Russian Math. Surveys 18, 85 (1964)
F. Baldovin, in Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann, C. Tsallis (Oxford University Press, New York, 2004); F. Baldovin, C. Tsallis, B. Schulze, Physica A 320, 184 (2003); F. Baldovin, Physica A 305, 124 (2002)
B.V. Chirikov Phys. Rep. 52, 263 (1979)
F. Baldovin, E. Brigatti, C. Tsallis, Phys. Lett. A 320, 254 (2004); F. Baldovin, Physica A 342, 119 (2004)
F. Baldovin, L.G. Moyano, A.P. Majtey, A. Robledo, C. Tsallis, Physica A 340, 205 (2004)
V. Latora, M. Baranger, Phys. Rev. Lett. 82, 520 (1999)
C. Tsallis, Quimica Nova 17, 468 (1994)
G. Benettin, L. Galgani, A. Giorgilli, J.M. Strelcyn, Meccanica 15, 21 (1980); see, e.g., [1]
F. Baldovin, C. Tsallis, in progress
B.M. Boghosian, P.J. Love, P.V. Coveney, I.V. Karlin, S. Succi, J. Yepez, Phys. Rev. E 68, 025103(R) (2003); B.M. Boghosian, P. Love, J. Yepez, P.V. Coveney, Physica D 193, 169 (2004)
G.A. Tsekouras, A. Provata, C. Tsallis, Phys. Rev. E 69, 016120 (2004); C. Anteneodo, Eur. Phys. J. B 42, 271 (2004)
C. Anteneodo, C. Tsallis, Phys. Rev. Lett. 80, 5313 (1998)
B.J.C. Cabral, C. Tsallis, Phys. Rev. E 66, 065101(R) (2002)
V. Latora, A. Rapisarda, C. Tsallis, Phys. Rev. E 64, 056134 (2001); F.D. Nobre, C. Tsallis, Phys. Rev. E 68, 036115 (2003); F.D. Nobre, C. Tsallis, Physica A 344, 587 (2004)
C. Beck, Physica A 305, 209 (2002)
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Añaños, G., Baldovin, F. & Tsallis, C. Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach. Eur. Phys. J. B 46, 409–417 (2005). https://doi.org/10.1140/epjb/e2005-00269-1
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DOI: https://doi.org/10.1140/epjb/e2005-00269-1