Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mather sets for sequences of matrices and applications to the study of
  joint spectral radii   The joint spectral radius of a compact set of d-times-d matrices is defined
?to be the maximum possible exponential growth rate of products of matrices
drawn from that set. In this article we investigate the ergodic-theoretic
structure of those sequences of matrices drawn from a given set whose products
grow at the maximum possible rate. This leads to a notion of Mather set for
matrix sequences which is analogous to the Mather set in Lagrangian dynamics.
We prove a structure theorem establishing the general properties of these
Mather sets and describing the extent to which they characterise matrix
sequences of maximum growth. We give applications of this theorem to the study
of joint spectral radii and to the stability theory of discrete linear
inclusions.
  These results rest on some general theorems on the structure of orbits of
maximum growth for subadditive observations of dynamical systems, including an
extension of the semi-uniform subadditive ergodic theorem of Schreiber, Sturman
and Stark, and an extension of a noted lemma of Y. Peres. These theorems are
presented in the appendix.

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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: chem-ph