Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal Lyapunov exponents and principal Floquet spaces of positive
  random dynamical systems. I. General theory   This is the first of a series of papers concerned with principal Lyapunov
exponents and principal Floquet subspaces of positive random dynamical systems
in ordered Banach spaces. It focuses on the development of general theory.
First, the notions of generalized principal Floquet subspaces, generalized
principal Lyapunov exponents, and generalized exponential separations for
general positive random dynamical systems in ordered Banach spaces are
introduced, which extend the classical notions of principal Floquet subspaces,
principal Lyapunov exponents, and exponential separations for strongly positive
deterministic systems in strongly ordered Banach to general positive random
dynamical systems in ordered Banach spaces. Under some quite general
assumptions, it is then shown that a positive random dynamical system in an
ordered Banach space admits a family of generalized principal Floquet
subspaces, a generalized principal Lyapunov exponent, and a generalized
exponential separation. We will consider in the forthcoming parts applications
of the general theory developed in this part to positive random dynamical
systems arising from a variety of random mappings and differential equations,
including random Leslie matrix models, random cooperative systems of ordinary
differential equations, and random parabolic equations.

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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
16
The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat