Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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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  • [1] Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
  • [2] J. L. Synge and A. Schild, Tensor Calculus, Mathematical Expositions, no. 5, University of Toronto Press, Toronto, Ont., 1949. MR 0033165
  • [3] E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963, Geometry of Riemannian spaces, Math. Sci. Press, 1983
  • [4] C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960, pp. 226–793; appendix, pp. 794–858. With an appendix on tensor fields by J. L. Ericksen. MR 0118005
  • [5] A. Cemal Eringen (ed.), Continuum physics. Vol II, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Continuum mechanics of single-substance bodies. MR 0468444
  • [6] David Lovelock and Hanno Rund, Tensor, differential forms, and variational principles, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1975. Pure and Applied Mathematics. MR 0474046
  • [7] 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)
  • [8] V. I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210 (Russian). MR 0240280
  • [9] B. S. Berger and M. Rokni, Lyapunov exponents and continuum kinematics, Internat. J. Engrg. Sci. 25 (1987), no. 10, 1251–1257. MR 912603, https://doi.org/10.1016/0020-7225(87)90045-0
  • [10] E. N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sci. 20, 130-141 (1963)
  • [11] O. E. Rossler, An equation for continuous chaos, Phys. Lett. 57A, 397-398 (1976)
  • [12] O. E. Rössler, An equation for hyperchaos, Phys. Lett. A 71 (1979), no. 2-3, 155–157. MR 588951, https://doi.org/10.1016/0375-9601(79)90150-6
  • [13] A. Wolf, B. Swift, H. L. Swinney, J. A. Vastand, Determining Lyapunov exponents from a time series, Physica 16D, 285-317 (1985)
  • [14] Ippei Shimada and Tomomasa Nagashima, A numerical approach to ergodic problem of dissipative dynamical systems, Progr. Theoret. Phys. 61 (1979), no. 6, 1605–1616. MR 539440, https://doi.org/10.1143/PTP.61.1605

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DOI: https://doi.org/10.1090/qam/917027
Article copyright: © Copyright 1987 American Mathematical Society

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