Covariant Lyapunov vectors

Understand

The recent years have witnessed a growing interest for covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems.

• Here we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets' theorem for the properties of the CLVs.
• We then present a detailed description of a "dynamical" algorithm to compute the CLVs and show that it generically converges exponentially in time.
• We also discuss its numerical performance and compare it with other algorithms presented in literature.