Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic entropy of sign-stable mutation loops   We introduce a property of mutation loops, called the sign stability, with a
focus on an asymptotic behavior of the iteration of the tropical
$\mathcal{X}$-transformation. A sign-stable mutation loop has a numerical
invariant which we call the cluster stretch factor, in analogy with that of a
pseudo-Anosov mapping class on a marked surface. We compute the algebraic
entropies of the cluster $\mathcal{A}$- and $\mathcal{X}$-transformations
induced by a sign-stable mutation loop, and conclude that these two coincide
with the logarithm of the cluster stretch factor.

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The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg