Lyapunov exponents and subspace evolution
Authors:
M. Rokni and B. S. Berger
Journal:
Quart. Appl. Math. 45 (1987), 789-793
MSC:
Primary 34D05; Secondary 34C35, 58F10
DOI:
https://doi.org/10.1090/qam/917027
MathSciNet review:
917027
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Abstract: Differential equations are derived which describe the evolution of area tensors and normals associated with the subspaces of an $n$-dimensional Euclidean phase space, ${E_n}$. These provide computational methods for determining the Lyapunov exponents of continuous dynamical systems.
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A. Wolf, B. Swift, H. L. Swinney, J. A. Vastand, Determining Lyapunov exponents from a time series, Physica 16D, 285–317 (1985)
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J. Hale, Ordinary differential equations, Krieger Pub. Co., 1982
J. L. Synge and A. Schild, Tensor calculus, University of Toronto Press, 1962
E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963, Geometry of Riemannian spaces, Math. Sci. Press, 1983
C. Truesdell and R. A. Toupin, Classical field theories, Springer, 1960
A. C. Eringen, Continuum physics, Vol. II, Academic Press, 1975
D. Lovelock and H. Rund, Tensors, differential forms and variational principles, J. Wiley, New York, 1975
G. Benettin, L. Galagani, A. Giorgilli, J. Strelcyn, Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; method for computing all of them, Meccanica 15, 9–20 (1980)
V. I. Oseledec, A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19, 197–231 (1968)
B. S. Berger and M. Rokni, Lyapunov exponents and continuum kinematics, Int. J. Eng. Sci. 25, 1079–1084 (1987)
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)
O. E. Rossler, An equation for hyperchaos, Phys. Lett. 71A, 155–157 (1979)
A. Wolf, B. Swift, H. L. Swinney, J. A. Vastand, Determining Lyapunov exponents from a time series, Physica 16D, 285–317 (1985)
I. Shimada, T. Nagashima, A numerical approach to the ergodic problem of dissipative dynamical systems, Prog. in Theoretical Physics 61, 6, 1605–1616 (1979)
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Article copyright:
© Copyright 1987
American Mathematical Society