Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Entropy of Braids on the Torus   A fast method is presented for computing the topological entropy of braids on
the torus. This work is motivated by the need to analyze large braids when
studying two-dimensional flows via the braiding of a large number of particle
trajectories. Our approach is a generalization of Moussafir's technique for
braids on the sphere. Previous methods for computing topological entropies
include the Bestvina--Handel train-track algorithm and matrix representations
of the braid group. However, the Bestvina--Handel algorithm quickly becomes
computationally intractable for large braid words, and matrix methods give only
lower bounds, which are often poor for large braids. Our method is
computationally fast and appears to give exponential convergence towards the
exact entropy. As an illustration we apply our approach to the braiding of both
periodic and aperiodic trajectories in the sine flow. The efficiency of the
method allows us to explore how much extra information about flow entropy is
encoded in the braid as the number of trajectories becomes large.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th