Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive Lyapunov exponent by a random perturbation   We study the effect of a random perturbation on a one-parameter family of
dynamical systems whose behavior in the absence of perturbation is ill
understood. We provide conditions under which the perturbed system is ergodic
and admits a positive Lyapunov exponent, with an explicit lower bound, for a
large and controlled set of parameter values.

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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: eess