Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On irreducibility of Oseledets subspaces   For a cocycle of invertible real $n$-by-$n$ matrices, the Multiplicative
Ergodic Theorem gives an Oseledets subspace decomposition of $\mathbb{R}^n$;
that is, above each point in the base space, $\mathbb{R}^n$ is written as a
direct sum of equivariant subspaces, one for each Lyapunov exponent of the
cocycle. It is natural to ask if these summands may be further decomposed into
equivariant subspaces; that is, if the Oseledets subspaces are reducible. We
prove a theorem yielding sufficient conditions for irreducibility of the
trivial equivariant subspaces $\mathbb{R}^2$ and $\mathbb{C}^2$ for
$O_2(\mathbb{R})$-valued cocycles and give explicit examples where the
conditions are satisfied.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys