Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Least squares approximation of Lyapunov exponents

Authors: B. S. Berger and M. Rokni
Journal: Quart. Appl. Math. 47 (1989), 505-508
MSC: Primary 34D05; Secondary 58F11, 65D15
DOI: https://doi.org/10.1090/qam/1012272
MathSciNet review: MR1012272
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Discrete least squares approximations are shown to converge for the Lyapunov exponents of dynamical systems. Numerical examples demonstrate the approximation's utility.

References [Enhancements On Off] (What's this?)

  • [1] J. Hale, Ordinary Differential Equations, Krieger Pub. Co., 1982 MR 587488
  • [2] G. Benettin, L. Galagani, A. Giorgilli, and J. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; method for computing all of them, Meccanica 15, 9-30 (1980)
  • [3] V. I. Oseledec, A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19, 197-231 (1968) MR 0240280
  • [4] M. Rokni and B. S. Berger, Lyapunov exponents and subspace evolution, Quart. Appl. Math. 45, 789-793 (1987) MR 917027
  • [5] L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, 1971 MR 0350089
  • [6] A. Wolf, B. Swift, H. L. Swinney, and J. A. Vastand, Determining Lyapunov exponents from time series, Physica 16D, 285-317 (1985)
  • [7] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, NBS, 55, 1965
  • [8] H. T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover Pub., 1962 MR 0181773
  • [9] E. N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sci. 20, 130-141 (1963)
  • [10] O. E. Rossler, An equation for continuous chaos, Phys. Lett. 57A, 397-398 (1976)
  • [11] B. S. Berger and M. Rokni, Lyapunov exponents and continuum kinematics, Int. J. Engrg. Sci. 25, 1251-1257 (1987) MR 912603
  • [12] N. G. De Bruijn, Asymptotic Methods in Analysis, North Holland Pub. Co., 1961 MR 0177247
  • [13] F. W. J. Olver, Asymptotics and Special Functions, Academic Press, 1974 MR 0435697
  • [14] B. S. Berger and M. Rokni, Lyapunov exponents and the evolution of normals, Int. J. Engrg. Sci. 25, 1393-1396 (1987) MR 921359

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34D05, 58F11, 65D15

Retrieve articles in all journals with MSC: 34D05, 58F11, 65D15

Additional Information

DOI: https://doi.org/10.1090/qam/1012272
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society