Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extension of the Lyapunov analysis for the predictability problem   The predictability problem for systems with different characteristic time
scales is investigated. It is shown that even in simple chaotic dynamical
systems, the leading Lyapunov exponent is not sufficient to estimate the
predictability time. This fact is due the saturation of the error on the fast
components of the system which therefore do not contribute to the exponential
growth of the error at large errors. It is proposed to adopt a generalization
of the Lyapunov exponent which is based on the natural concept of error growing
time at finite error size. The method is first illustrated on a simple
numerical model obtained by coupling two Lorenz systems with different time
scales. As a more realistic example, this analysis is then applied to a toy
model of Atmospheric circulation recently introduced by Lorenz.

2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol