TY - JOUR

T1 - Infinite invariant density determines statistics of time averages for weak chaos

AU - Korabel, N.

AU - Barkai, E.

PY - 2012/2/10

Y1 - 2012/2/10

N2 - Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x̄. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.

AB - Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x̄. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.

UR - http://www.scopus.com/inward/record.url?scp=84856908729&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.108.060604

DO - 10.1103/PhysRevLett.108.060604

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C2 - 22401047

AN - SCOPUS:84856908729

SN - 0031-9007

VL - 108

JO - Physical Review Letters

JF - Physical Review Letters

IS - 6

M1 - 060604

ER -