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Liapunov Multipliers and Decay of Correlations in Dynamical Systems

Pierre Collet·Jean-Pierre Eckmann
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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 $C^1$, the essential decorrelation rate is never faster than what is dictated by the {\em smallest} unstable Liapunov multiplier.

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Pierre Collet, Jean-Pierre Eckmann. 2003-03-04. Liapunov Multipliers and Decay of Correlations in Dynamical Systems. https://doi.org/10.1023/b%3Ajoss.0000019817.71073.61

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