An asymptotically exact stopping rule for the numerical computation of the Lyapunov spectrum

Chaos, Solitons and Fractals

Volumn 7, Issue 8, 1996, Pages 1213-1225

  Ezzine, Jelel ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042091880     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/0960-0779(95)00107-7     Document Type: Article

References (14)

1. L. Arnold and V. Wihstutz (eds), Lyapunov Exponents, Lecture Notes in Mathematics, No. 1186. Springer, NY (1986).
2. A. J. Lichtenberg and M. A. Liebermann, Regular and Chaotic Dynamics, Second Edition, Applied Mathematics Sciences, Vol. 38. Springer, NY (1992).
3. D. Talay, Approximation of upper Lyapunov exponents of bilinear stochastic differential systems, SIAM, J. on Num. Anal. 28(4), 1141 (1991).
4. J. P. Eckmann and D. Ruelle, Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems, IHES/P/90/11 (1990).
5. H. Furstenberg and R. Kesten, Product of random matrices. Ann. Math. Stats. 31, 457 (1960).
6. J. Ezzine, On the stabilization and control of hybrid systems, Ph.D. thesis, Georgia Institute of Technology, (June 1989).
7. M. Katz and A. J. Thomasian, An exponential bound for functions of a Markov chain, Ann. Math. Stats. 31, 470 (1960).
8. J. Ezzine, On a practical stopping rule for the numerical computation of the Lyapunov spectrum, Proc. IEEE 11th ACC, Chicago, IL (June 1992).
9. J. L. Doob, Stochastic Processes. John Wiley and Sons, NY (1953).
10. A. Lasota and J. A. York, On the existence of invariant measures for piecewise monotonic transformations, Trans. Am. Math. Soc. 186, 481 (1973).
11. M. Barnsley, Fractals Everywhere. Academic Press, NY (1988).
12. G. Nicolis, Finite coarse-graining and Chapman-Kolmogorov equation in conservative dynamical systems, Chaos, Solitons & Fractals 1(1), 25 (1991).
13. A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16, 285 (1985).
14. J. W. Aronson, CHAOS, A SUN-based program for analyzing chaotic systems, Computers in Physics 408 (1990).