Abstract
The existence of a thermodynamic limit of the distribution of Liapunov exponents is numerically verified in a large class of symplectic models, ranging from Hamiltonian flows to maps and products of random matrices. In the highly chaotic regime this distribution is approximately model-independent. Near an integrable limit only a few exponents give a relevant contribution to the Kolmogorov-Sinai entropy.
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References
J. P. Eckmann and D. Ruelle,Rev. Mod. Phys. 57:617 (1985).
R. Livi, M. Pettini, S. Ruffo, M. Sparpaglione, and A. Vulpiani,Phys. Rev. A 31:1039 (1985); R. Livi, M. Pettini, S. Ruffo, and A. Vulpiani,Phys. Rev. A 31:2740 (1985).
Ya. B. Pesin,Dokl. Akad. Nauk 226:774 (1976).
R. Livi, A. Politi, and S. Ruffo,J. Phys. A 19:2033 (1986).
A. B. Rechester, N. M. Rosenblut, and R. B. White,Phys. Rev. Lett. 42:1247 (1979); G. Benettin,Physica 13D:211 (1984).
G. Paladin and A. Vulpiani,J. Phys. A 19:1881 (1986); G. Parisi and A. Vulpiani,J. Phys. A 19:L425 (1986); B. Derrida and E. Gardner,J. Phys. (Paris) 45:1283 (1984).
C. M. Newman,Commun. Math. Phys. 103:121 (1986); “Liapunov exponents for some products of random matrices: Exact expressions and asymptotic distributions,” to appear inRandom Matrices and Their Applications, J. E. Cohen, M. Kesten and C. M. Newman (eds.), AMS Series in Contemporary Mathematics.
J. Carr,Applications of Centre Manifold Theory (Springer, New York, 1981).
G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn,Meccanica 15:9, 15 (1980).
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Livi, R., Politi, A., Ruffo, S. et al. Liapunov exponents in high-dimensional symplectic dynamics. J Stat Phys 46, 147–160 (1987). https://doi.org/10.1007/BF01010337
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DOI: https://doi.org/10.1007/BF01010337