Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaos and frequent hypercyclicity for composition operators   The notions of chaos and frequent hypercyclicity enjoy an intimate
relationship in linear dynamics. Indeed, after a series of partial results, it
was shown by Bayart and Rusza in 2015 that for backward weighted shifts on
$\ell_p(\mathbb{Z})$, the notions chaos and frequent hypercyclicity coincide.
It is with some effort that one shows that these two notions are distinct.
Bayart and Grivaux in 2007 constructed a non-chaotic frequently hypercyclic
weighted shift on $c_0$. It was only in 2017 that Menet settled negatively
whether every chaotic operator is frequently hypercylic. In this article, we
show that for a large class of composition operators on $L^p$-spaces the
notions of chaos and frequent hypercyclicity coincide. Moreover, in this
particular class an invertible operator is frequently hypercyclic if and only
if its inverse is frequently hypercyclic. This is in contrast to a very recent
result of Menet where an invertible frequently hypercyclic operator on $\ell_1$
whose inverse is not frequently hypercyclic is constructed.

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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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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: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int