Least squares approximation of Lyapunov exponents

Berger, B. S.; Rokni, M.

doi:10.1090/qam/1012272

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

Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488

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)

V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210 (Russian). MR 0240280
M. Rokni and B. S. Berger, Lyapunov exponents and subspace evolution, Quart. Appl. Math. 45 (1987), no. 4, 789–793. MR 917027, DOI https://doi.org/10.1090/S0033-569X-1987-0917027-9
Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, 3rd ed., Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 16. MR 0350089

A. Wolf, B. Swift, H. L. Swinney, and J. A. Vastand, Determining Lyapunov exponents from time series, Physica 16D, 285–317 (1985)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, NBS, 55, 1965

Harold T. Davis, Introduction to nonlinear differential and integral equations, Dover Publications, Inc., New York, 1962. MR 0181773

E. N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sci. 20, 130–141 (1963)

O. E. Rossler, An equation for continuous chaos, Phys. Lett. 57A, 397–398 (1976)

B. S. Berger and M. Rokni, Lyapunov exponents and continuum kinematics, Internat. J. Engrg. Sci. 25 (1987), no. 10, 1251–1257. MR 912603, DOI https://doi.org/10.1016/0020-7225%2887%2990045-0
N. G. de Bruijn, Asymptotic methods in analysis, 2nd ed., North-Holland Publishing Co., Amsterdam; P. Noordhoff Ltd., Groningen, 1961. Bibliotheca Mathematica, Vol. IV. MR 0177247
F. W. J. Olver, Asymptotics and special functions, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR 0435697
B. S. Berger and M. Rokni, Lyapunov exponents and the evolution of normals, Internat. J. Engrg. Sci. 25 (1987), no. 11-12, 1393–1396. MR 921359, DOI https://doi.org/10.1016/0020-7225%2887%2990017-6