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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
C2 - 22401047
AN - SCOPUS:84856908729
SN - 0031-9007
VL - 108
JO - Physical Review Letters
JF - Physical Review Letters
IS - 6
M1 - 060604
ER -