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Zbl 0910.34055
Christiansen, F.; Rugh, H.H.
Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization. (English)
[J] Nonlinearity 10, No.5, 1063-1072 (1997). ISSN 0951-7715; ISSN 1361-6544/e

The authors propose an interesting method to calculate the Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. The dynamical system is augmented with an orthonormal frame and a Lyapunov vector, such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. It is shown that the method is strongly stable when a properly chosen stability parameter is sufficiently large. Finally, the method is applied to the Lorentz equations and a 3-DOF Hamiltonian system.
[A.Steindl (Wien)]

MSC 2000:: *34D08 Lyapunov exponents
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: Lyapunov spectrum; dynamical system; chaos; stability; orthogonalization

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