Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical properties of the negative beta transformation   We analyse dynamical properties of the negative beta transformation, which
has been studied recently by Ito and Sadahiro. Contrary to the classical beta
transformation, the density of the absolutely continuous invariant measure of
the negative beta transformation may be zero on certain intervals. By
investigating this property in detail, we prove that the
$(-\beta)$-transformation is exact for all $\beta>1$, confirming a conjecture
of G\'ora, and intrinsic, which completes a study of Faller. We also show that
the limit behaviour of the $(-\beta)$-expansion of 1 when $\beta$ tends to 1 is
related to the Thue-Morse sequence. A consequence of the exactness is that
every Yrrap number, which is a $\beta>1$ such that the $(-\beta)$-expansion of
1 is eventually periodic, is a Perron number. This extends a well-known
property of Parry numbers. However, the set of Parry numbers is different from
the set of Yrrap numbers.

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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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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: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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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: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an