On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
- 1 February 1997
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 34 (1) , 402-423
- https://doi.org/10.1137/s0036142993247311
Abstract
In this paper, we consider discrete and continuous QR algorithms for computing all of the Lyapunov exponents of a regular dynamical system. We begin by reviewing theoretical results for regular systems and present general perturbation results for Lyapunov exponents. We then present the algorithms, give an error analysis of them, and describe their implementation. Finally, we give several numerical examples and some conclusions.Keywords
This publication has 19 references indexed in Scilit:
- Computational Techniques for Real Logarithms of MatricesSIAM Journal on Matrix Analysis and Applications, 1996
- Computation of a few Lyapunov exponents for continuous and discrete dynamical systemsApplied Numerical Mathematics, 1995
- A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEsSIAM Journal on Scientific Computing, 1994
- Unitary Integrators and Applications to Continuous Orthonormalization TechniquesSIAM Journal on Numerical Analysis, 1994
- Aspects of backward error analysis of numerical ODEsJournal of Computational and Applied Mathematics, 1993
- Comparison of Different Methods for Computing Lyapunov ExponentsProgress of Theoretical Physics, 1990
- Remarks on linear differential systems with measurable coefficientsProceedings of the American Mathematical Society, 1987
- Ergodic theory of chaos and strange attractorsReviews of Modern Physics, 1985
- An automatic orthonormalization method for solving stiff boundary-value problemsJournal of Computational Physics, 1983
- Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: TheoryMeccanica, 1980