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Characterizing dynamics with covariant Lyapunov vectors

Banff International Research Station for Mathematical Innovation and Discovery

Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) as an important tool for characterizing chaotic dynamics in high dimensional system. CLVs define an intrinsic, non orthogonal basis at each point in phase space which is covariant with the dynamics and coincides with the so called Oseledets splitting for invertible systems. After a brief introduction, we discuss in details the dynamical algorithm we have introduced to e\0ciently compute CLV’s and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate selected applications; in particular, CLV’s have been used to characterize the collective dynamics of globally coupled systems, to quantify the degree of hyperbolicity, and to evaluate the number of e↵ective degrees of freedom in chaotic, spatially extended dissipative systems such as the Kuramoto-Sivashinsky equation.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: University of Aberdeen

2015-07-22

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54130

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/