Dr Politi make a nice, comprehensible, and concise review of Lyapunov exponents in application to dynamical system studies.
My only suggestion is to add a section describing (briefly, but with references to other scholarpedia articles or other sources) other application of this concept - in the theory of stochastic processes, in statistical physics (transfer matrix approach), etc.
- A Pikovsky
Following the advice of the reviewer, I have made the following modifications:
1) I introduce the Lyapunov exponents directly with reference to
the linear evolution and mention that they can arise in generic contexts such as linear stochastic differential equations. Reference to deterministic dynamical systems follows.
2) I have added a final section, where a few applications are
briefly discussed (localization and advection, besides mentioning synchronization).
3) I have added specific references about the above mentioned
subjects plus some suitable internal references that are separately listed in the end.