Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characteristic matrix functions for delay differential equations with
  symmetry   A characteristic matrix function captures the spectral information of a
bounded linear operator in a matrix-valued function. In this article, we
consider a delay differential equation with one discrete time delay and assume
this equation is equivariant with respect to a compact symmetry group. Under
this assumption, the delay differential equation can have discrete wave
solutions, i.e. periodic solutions that have a discrete group of
spatio-temporal symmetries. We show that if a discrete wave solution has a
period that is rationally related to the time delay, then we can determine its
stability using a characteristic matrix function. The proof relies on
equivariant Floquet theory and results by Kaashoek and Verduyn Lunel on
characteristic matrix functions for classes of compact operators. We discuss
applications of our result in the context of delayed feedback stabilization of
periodic orbits.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ