Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cellular automata and substitutions in topological spaces defined via
  edit distances   The Besicovitch pseudo-metric is a shift-invariant pseudo-metric on the set
of infinite sequences, that enjoys interesting properties and is suitable for
studying the dynamics of cellular automata. They correspond to the asymptotic
behavior of the Hamming distance on longer and longer prefixes. Though dynamics
of cellular automata were already studied in the literature, we propose the
first study of the dynamics of substitutions. We characterize those that yield
a well-defined dynamical system as essentially the uniform ones. We also
explore a variant of this pseudo-metric, the Feldman pseudo-metric, where the
Hamming distance is replaced by the Levenshtein distance. Like in the
Besicovitch space, cellular automata are Lipschitz in this space, but here also
all substitutions are Lipschitz. In both spaces, we discuss equicontinuity of
these systems, and give a number of examples, and generalize our results to the
class of the dill maps, that embed both cellular automata and substitutions.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys