Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sensitivity of long periodic orbits of chaotic systems   The properties of long, numerically-determined periodic orbits of two
low-dimensional chaotic systems, the Lorenz equations and the
Kuramoto-Sivashinsky system in a minimal-domain configuration, are examined.
The primary question is to establish whether the sensitivity of period averaged
quantities with respect to parameter perturbations computed over long orbits
can be used as a sufficiently good proxy for the response of the chaotic state
to finite-amplitude parameter perturbations. To address this question, an
inventory of thousands of orbits at least two orders of magnitude longer than
the shortest admissible cycles is constructed. The expectation of period
averages, Floquet exponents and sensitivities over such set is then obtained.
It is shown that all these quantities converge to a limiting value as the orbit
period is increased. However, while period averages and Floquet exponents
appear to converge to analogous quantities computed from chaotic trajectories,
the limiting value of the sensitivity is not necessarily consistent with the
response of the chaotic state, similar to observations made with other
shadowing algorithms.

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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom