Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization. (English) Zbl 0910.34055

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.
Reviewer: A.Steindl (Wien)


34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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