Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: ${\mathcal F}$-Hypercyclic operators on Fr\' echet spaces   In this paper, we investigate ${\mathcal F}$-hypercyclicity of linear, not
necessarily continuous, operators on Fr\' echet spaces. The notion of lower
$(m_{n})$-hypercyclicity seems to be new and not considered elsewhere even for
linear continuous operators acting on Fr\' echet spaces. We pay special
attention to the study of $q$-frequent hypercyclicity, where $q\geq 1$ is an
arbitrary real number. We present several new concepts and results for lower
and upper densities in a separate section, providing also a great number of
illustrative examples and open problems.

14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas