Abstract
The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in \(\mathcal{C}^1\), the essential decorrelation rate is never faster than what is dictated by the smallest unstable Liapunov multiplier.
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Collet, P., Eckmann, JP. Liapunov Multipliers and Decay of Correlations in Dynamical Systems. Journal of Statistical Physics 115, 217–254 (2004). https://doi.org/10.1023/B:JOSS.0000019817.71073.61
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DOI: https://doi.org/10.1023/B:JOSS.0000019817.71073.61