Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Sturmian substitutions closed under derivation   Occurrences of a factor $w$ in an infinite uniformly recurrent sequence ${\bf
u}$ can be encoded by an infinite sequence over a finite alphabet. This
sequence is usually denoted ${\bf d_{\bf u}}(w)$ and called the derived
sequence to $w$ in ${\bf u}$. If $w$ is a prefix of a fixed point ${\bf u}$ of
a primitive substitution $\varphi$, then by Durand's result from 1998, the
derived sequence ${\bf d_{\bf u}}(w)$ is fixed by a primitive substitution
$\psi$ as well. For a non-prefix factor $w$, the derived sequence ${\bf d_{\bf
u}}(w)$ is fixed by a substitution only exceptionally. To study this phenomenon
we introduce a new notion: A finite set $M $ of substitutions is said to be
closed under derivation if the derived sequence ${\bf d_{\bf u}}(w)$ to any
factor $w$ of any fixed point ${\bf u}$ of $\varphi \in M$ is fixed by a
morphism $\psi \in M$. In our article we characterize the Sturmian
substitutions which belong to a set $M$ closed under derivation. The
characterization uses either the slope and the intercept of its fixed point or
its S-adic representation.

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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas