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- W1999700033 abstract "Using intermittent maps with infinite invariant measures, we investigate the universality of time-averaged observables under aging conditions. According to Aaronson's Darling-Kac theorem, in non-aged dynamical systems with infinite invariant measures, the distribution of the normalized time averages of integrable functions converges to the Mittag-Leffler distribution. This well known theorem holds when the start of observations coincides with the start of the dynamical processes. Introducing a concept of the aging limit where the aging time ${t}_{a}$ and the total measurement time $t$ goes to infinity while the aging ratio ${t}_{a}/t$ is kept constant, we obtain a novel distributional limit theorem of time-averaged observables integrable with respect to the infinite invariant density. Applying the theorem to the Lyapunov exponent in intermittent maps, we find that regular motions and a weakly chaotic behavior coexist in the aging limit. This mixed type of dynamics is controlled by the aging ratio and hence is very different from the usual scenario of regular and chaotic motions in Hamiltonian systems. The probability of finding regular motions in non-aged processes is zero, while in the aging regime it is finite and it increases when system ages." @default.
- W1999700033 created "2016-06-24" @default.
- W1999700033 creator A5049454633 @default.
- W1999700033 creator A5075146702 @default.
- W1999700033 date "2013-03-25" @default.
- W1999700033 modified "2023-09-26" @default.
- W1999700033 title "Aging generates regular motions in weakly chaotic systems" @default.
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- W1999700033 doi "https://doi.org/10.1103/physreve.87.032915" @default.
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