Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering of exponentially separating trajectories   It might be expected that trajectories for a dynamical system which has no
negative Lyapunov exponent (implying exponential growth of small separations
will not cluster together. However, clustering can occur such that the density
$\rho(\Delta x)$ of trajectories within distance $\Delta x$ of a reference
trajectory has a power-law divergence, so that $\rho(\Delta x)\sim \Delta
x^{-\beta}$ when $\Delta x$ is sufficiently small, for some $0<\beta<1$. We
demonstrate this effect using a random map in one dimension. We find no
evidence for this effect in the chaotic logistic map, and argue that the effect
is harder to observe in deterministic maps.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph