Computation of the Lyapunov spectrum for continuous-time dynamical systems and discrete maps. (English) Zbl 1062.37510
Summary: We describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov spectrum can be computed using fewer equations as compared to the computation of the full spectrum, there is no difficulty in evaluating degenerate Lyapunov spectra, the equations are straightforward to generalize to higher dimensions, and the minimal set of dynamical variables is used. Explicit proofs and other details not given in previous work are included here.
MSC:
| 37M25 | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 37D99 | Dynamical systems with hyperbolic behavior |
References:
| [1] | J.-P. Eckmann, Rev. Mod. Phys. 57 pp 617– (1985) · Zbl 0989.37516 · doi:10.1103/RevModPhys.57.617 |
| [2] | G. Bennetin, Phys. Rev. A 14 pp 2338– (1976) · doi:10.1103/PhysRevA.14.2338 |
| [3] | I. Shimada, Prog. Theor. Phys. 61 pp 1605– (1979) · Zbl 1171.34327 · doi:10.1143/PTP.61.1605 |
| [4] | A. Wolf, Physica D 16 pp 285– (1985) · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9 |
| [5] | K. Geist, Prog. Theor. Phys. 83 pp 875– (1990) · Zbl 1058.65512 · doi:10.1143/PTP.83.875 |
| [6] | S. Habib, Phys. Rev. Lett. 74 pp 70– (1995) · doi:10.1103/PhysRevLett.74.70 |
| [7] | F. Christiansen, Nonlinearity 10 pp 1063– (1997) · Zbl 0910.34055 · doi:10.1088/0951-7715/10/5/004 |
| [8] | S. Habib, in: Nonlinear Evolution Equations and Dynamical Systems, Proceedings of the 10th Workshop on Nonlinear Evolution Equations and Dynamical Systems, Los Alamos, New Mexico, 1994 (1995) |
| [9] | G. Rangarajan, Phys. Rev. Lett. 80 pp 3747– (1998) · doi:10.1103/PhysRevLett.80.3747 |
| [10] | G. H. Golub, in: Matrix Computations, 3rd ed. (1996) |
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