| We discuss covariant Lyapunov vectors (CLVs) in high dimensional dynamical systems. 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 Oseledec splitting for invertible systems. We will show that the statistical properties of CLVs differ from those of the vectors obtained from the standard orthogonalization procedure introduced by Benettin et al. and discuss recent results obtained by studying these new indicators. In particular, CLVs can be used to characterize the collective dynamics of globally coupled systems, to quantify the degree of hyperbolicity, and to evaluate the number of effective degrees of freedom in chaotic, spatially extended dissipative systems such as the Kuramoto-Sivashinsky equation. |
|