Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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   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.

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The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph