Eckhardt, Bruno; Yao, Demin Local Lyapunov exponents in chaotic systems. (English) Zbl 0781.58024 Physica D 65, No. 1-2, 100-108 (1993). The notion of local Lyapunov exponents (LLE) for dynamical systems is defined in the paper both for the systems with continuous time and for whose with discrete time. The results of the computer calculations of the LLE for some systems are discussed. Calculations are presented for the dissipative Lorenz system, conservative Chirikov-Taylor map, and for a 3D volume preserving flow. The results demonstrate that large fluctuations of the LLE’s around the long time average for an unstable trajectory take place. Reviewer: Y.P.Virchenko (Khar’kov) Cited in 19 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37D99 Dynamical systems with hyperbolic behavior Keywords:chaotic system; Chirikov-Taylor map; kinematic dynamo; Lyapunov exponents PDFBibTeX XMLCite \textit{B. Eckhardt} and \textit{D. Yao}, Physica D 65, No. 1--2, 100--108 (1993; Zbl 0781.58024) Full Text: DOI References: [1] Schuster, H. G., Deterministic Chaos (1988), VCH: VCH Weinheim [2] Grassberger, P.; Badii, R.; Politi, A., J. Stat. Phys., 51, 135 (1988) [3] Fujisaka, H., Progr. Theor. Phys., 70, 1264 (1983) [4] Haubs, G.; Haken, H., Z. Phys. B, 59, 459 (1985) [5] Ott, E.; Grebogi, C.; Yorke, J., Phys. Rev. Lett., 64, 1196 (1990) [6] Doerner, R.; Hübinger, B.; Martienssen, W.; Grossmann, S.; Thomae, S., Chaos, Solitons and Fractals, 1, 553 (1991) [7] Eckhardt, B.; Gomez-Llorente, J. M.; Pollak, E., Chem. Phys. Lett., 174, 325 (1990) [8] Sepulveda, M. A.; Badii, R.; Pollak, E., Phys. Rev. Lett., 63, 1226 (1989) [9] Bayly, B. J., Phys. Rev. Lett., 57, 2800 (1986) [10] Aref, H., J. Fluid Mech., 143, 1 (1984) [11] Khakhar, D. V.; Ottino, J. M., Phys. Fluids, 29, 3503 (1986) [12] Toda, M., Phys. Lett. A, 48, 335 (1974) [13] Brumer, P.; Duff, J. W., J. Chem. Phys., 65, 3566 (1976) [14] Tabor, M., Adv. Chem. Phys., 46, 73 (1981) [15] Eckhardt, B.; Louw, J. A.; Steeb, W.-H., Aust. J. Phys., 39, 331 (1986) [16] Nese, J. M., Physica D, 35, 237 (1989) [17] Lorenz, E. N., J. Atmos. Sci., 20, 130 (1963) [18] Chirikov, B. V., Phys. Rep., 52, 265 (1979) [19] Lichtenberg, A. J.; Lieberman, M. A., Regular and Stochastic Motion (1983), Springer: Springer New York, section 3.3b · Zbl 0506.70016 [20] Moffatt, H. K., Magnetic Fields Generation in Conducting Fluids (1978), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK · Zbl 0393.76063 [21] Dombre, T.; Frisch, U.; Greene, J. M.; Hénon, M.; Mehr, A.; Soward, A. M., J. Fluid Mech., 167, 353 (1986) [22] Galloway, D. J.; Frisch, U., Geophys. Astrophys. Fluid Dyn., 36, 53 (1986) [23] Bayly, B. J., Phys. Fluids, 31, 56 (1988) [24] Grebogi, C.; Hammel, S. M.; Yorke, J. A.; Sauer, T., Phys. Rev. Lett., 65, 1527 (1990) [25] Dresselhaus, E.; Tabor, M., J. Fluid Mech., 236, 415 (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.