Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local correlation entropy   Local correlation entropy, introduced by Takens in 1983, represents the
exponential decay rate of the relative frequency of recurrences in the
trajectory of a point, as the embedding dimension grows to infinity. In this
paper we study relationship between the supremum of local correlation entropies
and the topological entropy. For dynamical systems on graphs we prove that the
two quantities coincide. Moreover, there is an uncountable set of points with
local correlation entropy arbitrarily close to the topological entropy. On the
other hand, we construct a strictly ergodic subshift with positive topological
entropy having all local correlation entropies equal to zero. As a necessary
tool, we derive an expected relationship between the local correlation
entropies of a system and those of its iterates.

6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys