Characterizing dynamics with covariant Lyapunov vectors

Details Characterizing dynamics with covariant Lyapunov vectors Characterizing dynamics with covariant Lyapunov vectors

2007-06-04

arxiv.org/abs/0706.0510v1

Phys Rev Lett 99, 130601 (2007).

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, submitted to Physical Review letters

Scientific paper

10.1103/PhysRevLett.99.130601

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors. For spatially extended systems, the covariant Lyapunov vectors have localization properties and spatial Fourier spectra qualitatively different from those composing the orthonormalized basis obtained in the standard procedure used to calculate the Lyapunov exponents.

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