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Kolmogorov-Sinai entropy for locally coupled piecewise linear maps. (English) Zbl 0995.37004
Summary: We present analytical results for the Kolmogorov-Sinai entropy of a one-dimensional lattice of locally coupled piecewise linear maps, for some particular values of the coupling strength. Our results explain the numerically observed fact that the entropy of a lattice of chaotic maps increases for strong coupling.

37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI
[1] Kaneko, K., The coupled map lattice, (), 1
[2] Kaneko, K., Physica D, 34, 1, (1989)
[3] Lind, P.; Corte-Real, J.; Gallas, J.A.C., Physica A, 295, 297, (2001)
[4] Chaté, H.; Manneville, P., Physica D, 32, 409, (1988)
[5] de Souza Pinto, S.E.; Viana, R.L., Phys. rev. E, 61, 5154, (2000)
[6] J.P. Crutchfield, K. Kaneko, Phenomenology of spatio-temporal chaos, in: Hao Bain-Lin (Ed.), Directions in Chaos, Vol. 1, World Scientific, Singapore, 1987, p. 272.
[7] Kaneko, K., Physica D, 23, 436, (1986)
[8] Isola, S.; Politi, A.; Ruffo, S.; Torcini, A., Phys. lett. A, 143, 365, (1990)
[9] Ruelle, D., Chaotic evolution and strange attractors, (1989), Cambridge University Press Cambridge
[10] Kaneko, K., Physica D, 41, 137, (1990)
[11] Batista, A.M.; Viana, R.L., Phys. lett. A, 286, 134, (2001) · Zbl 0969.37519
[12] Shibata, H., Physica A, 292, 182-192, (2001)
[13] Tsallis, C.; Plastino, A.R.; Zheng, W.-M.; Lyra, M.L.; Tsallis, C.; Costa, U.M.S.; Lyra, M.L.; Plastino, A.R.; Tsallis, C., Chaos, solitons & fractals, Phys. rev. lett., Phys. rev. E, 56, 245, (1997)
[14] Montangero, S.; Fronzoni, L.; Grigolini, P., Phys. lett. A, 285, 81-87, (2001)
[15] A.M. Batista, S.E.S. Pinto, S.R. Lopes, R.L. Viana, Lyapunov spectrum and synchronization of piecewise linear map lattices with power-law coupling, Phys. Rev. E (2002), to be published.
[16] Schuster, H.G., Deterministic chaos, (1988), VCH Weinheim
[17] Davis, P.J., Circulant matrices, (1979), Wiley-Interscience New York · Zbl 0418.15017
[18] Carretero-González, R.; Ørstavik, S.; Huke, J.; Broomhead, D.S.; Stark, J., Chaos, 9, 466, (1999)
[19] Pesin, Y.B., Russ. math. surv., 32, 55, (1977)
[20] Ruelle, D., Bol. soc. brasil mat., 9, 83, (1978)
[21] Bricmont, J.; Kupiainen, A., Physica D, 103, 18-33, (1997)
[22] Keller, G.; Künzle, M.; Volevich, D.L.; Volevich, D.L., Ergodic theory dyn. systems, Russ. acad. dokl. math., Russ. acad. math. sbornik, 79, 347-363, (1994)
[23] Alligood, K.A.; Sauer, T.; Yorke, J.A., Chaos. an introduction to dynamical systems, (1997), Springer New York
[24] Boldrighini, C.; Bunimovich, L.A.; Cosimi, G.; Frigio, S.; Pellegrinotti, A., J. statist. phys., 102, 1271, (2001)
[25] Gradshteyn, S.; Ryzhik, I.M., Table of integrals, series and products, (1994), Academic Press New York · Zbl 0918.65002
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