2,338 research outputs found
Infinite Invariant Density Determines Statistics of Time Averages for Weak Chaos
Weakly chaotic non-linear maps with marginal fixed points have an infinite
invariant measure. Time averages of integrable and non-integrable 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 non-integrable observables, for example the
time average position of the particle. 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.Comment: 5 pages, 3 figure
Be Just to One Another: Preliminary Thoughts on Civility, Moral Character, and Professionalism
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