Dynamical observables in chaotic systems share the same large deviation rate function when their g functions differ by a 'derived' function, making derived observables have N-independent symmetric distributions.
Grassberger, Information flow and maximum entropy measures for 1-D maps, Physica D: Nonlinear Phenomena 14, 365 (1985)
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Remarkable similarities in distributions of dynamical observables in chaotic systems
Dynamical observables in chaotic systems share the same large deviation rate function when their g functions differ by a 'derived' function, making derived observables have N-independent symmetric distributions.