Infinite invariant density determines statistics of time averages for weak chaos

N. Korabel, E. Barkai

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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.

Original languageEnglish
Article number060604
JournalPhysical Review Letters
Volume108
Issue number6
DOIs
StatePublished - 10 Feb 2012

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