Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean dimension of continuous cellular automata   We investigate the mean dimension of a cellular automaton (CA for short) with
a compact non-discrete space of states.
  A formula for the mean dimension is established for (near) strongly
permutative, permutative algebraic and unit one-dimensional automata. In higher
dimensions, a CA permutative algebraic or having a spaceship has infinite mean
dimension. However, building on Meyerovitch's example, we give an example of
algebraic surjective cellular automaton with positive finite mean dimension.

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The categories of this paper are: physics
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas