Beyond Lyapunov

Details Beyond Lyapunov Beyond Lyapunov

2010-08-16

arxiv.org/abs/1008.2664v2

Nonlinear Sciences

Chaotic Dynamics

15 pages Latex

Scientific paper

Ergodic parameters like the Lyapunov and the conditional exponents are global functions of the invariant measure, but the invariant measure itself contains more information. A more complete characterization of the dynamics by new families of ergodic parameters is discussed, as well as their relation to the dynamical R\'{e}nyi entropies and measures of self-organization. A generalization of the Pesin formula is derived which holds under some weak correlation conditions.

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