New method for computing finite-time Lyapunov exponents.
We present a novel method for computing finite-time Lyapunov exponents and vectors, via generalizing a correction given by Goldhirsch, Sulem, and Orszag [Physica (Amsterdam) 27D, 311 (1987)]] into higher-order corrections. This method is a generalized LR method, which is, in contrast to the existing methods, applicable to multidimensional systems with degenerate spectra. The efficiency and accuracy is demonstrated by applying it to multidimensional dynamical systems. Without these corrections, we could not accurately detect, as an example, the coexistence of qualitatively different Lyapunov instabilities along a trajectory for a multidimensional oscillator system.
Okushima
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Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan.