Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative periodic orbits form the backbone of turbulent pipe flow   Chaotic dynamics of low-dimensional systems, such as Lorenz or R\"ossler
flows, is guided by the infinity of periodic orbits embedded in their strange
attractors. Whether this also be the case for the infinite-dimensional dynamics
of Navier--Stokes equations has long been speculated, and is a topic of ongoing
study. Periodic and relative periodic solutions have been shown to be involved
in transitions to turbulence. Their relevance to turbulent
dynamics---specifically, whether periodic orbits play the same role in
high-dimensional nonlinear systems like the Navier--Stokes equations as they do
in lower-dimensional systems---is the focus of the present investigation. We
perform here a detailed study of pipe flow relative periodic orbits with
energies and mean dissipations close to turbulent values. We outline several
approaches to reduction of the translational symmetry of the system. We study
pipe flow in a minimal computational cell, and report a library of invariant
solutions found with the aid of the method of slices. Detailed study of the
unstable manifolds of a sample of these solutions is consistent with the
picture that relative periodic orbits are embedded in the chaotic saddle and
that they guide the turbulent dynamics.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-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: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th