Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean Li-Yorke chaos in Banach spaces   We investigate the notion of mean Li-Yorke chaos for operators on Banach
spaces. We show that it differs from the notion of distributional chaos of type
2, contrary to what happens in the context of topological dynamics on compact
metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only
if it has an absolutely mean irregular vector. As a consequence, absolutely
Ces\`aro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke
chaos is shown to be equivalent to the existence of a dense (or residual) set
of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke
chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional
closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a
sufficient condition for the existence of a dense absolutely mean irregular
manifold are also obtained. Moreover, we construct an example of an invertible
hypercyclic operator $T$ such that every nonzero vector is absolutely mean
irregular for both $T$ and $T^{-1}$. Several other examples are also presented.
Finally, mean Li-Yorke chaos is also investigated for $C_0$-semigroups of
operators on Banach spaces.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol