Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On dynamics of graph maps with zero topological entropy   We explore the dynamics of graph maps with zero topological entropy. It is
shown that a continuous map $f$ on a topological graph $G$ has zero topological
entropy if and only if it is locally mean equicontinuous, that is the dynamics
on each orbit closure is mean equicontinuous. As an application, we show that
Sarnak's M\"obius Disjointness Conjecture is true for graph maps with zero
topological entropy. We also extend several results known in interval dynamics
to graph maps. We show that a graph map has zero topological entropy if and
only if there is no $3$-scrambled tuple if and only if the proximal relation is
an equivalence relation; a graph map has no scrambled pairs if and only if it
is null if and only if it is tame.

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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio