Comment on "Shadowability of Statistical Averages in Chaotic Systems" by Y.C. Lai, Z. Liu, G.W. Wei, and C.H. Lai, Phys. Rev. Lett. 89, 184101
Abstract
Description
Lai {\it et al.} \cite{Lai:2002} investigate systems with a stable periodic orbit and a coexisting chaotic saddle. They claim that, by adding white Gaussian noise (GN), averages change with an algebraic scaling law above a certain noise threshold and argue that this leads to a breakdown of shadowability of averages. Here, we show that (i) shadowability is not well defined and even if it were, no breakdown occurs. We clarify misconceptions on (ii) thresholds for GN. We further point out (iii) misconceptions on the effect of noise on averages. Finally, we show that (iv) the lack of a proper threshold can lead to any (meaningless) scaling exponent.
Phys. Rev. Lett., to be published; first version of reply rejected
Phys. Rev. Lett., to be published; first version of reply rejected