Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The role of periodic orbits and bubbles of chaos during the transition
  to turbulence   Starting with turbulence that explores a wide region in phase space, we
discover several relative periodic orbits (RPOs) embedded within a subregion of
the chaotic turbulent saddle. We also extract directly from simulation, several
travelling waves (TWs). These TWs together with the RPOs are unstable states
and are believed to provide the skeleton of the chaotic saddle. Earlier studies
have shown that such invariant solutions can help to explain wall bounded shear
flows, and a finite subset of them are expected to dominate the dynamics
(Faisst & Eckhardt 2003; Pringle & Kerswell 2007; Hof et al. 2004). The
introduction of symmetries is typically necessary to facilitate this approach.
Applying only the shift-reflect symmetry, the geometry is less constrained than
previous studies in pipe flow. A 'long-period' RPO is identified that is only
very weakly repelling. Turbulent trajectories are found to frequently approach
and frequently shadow this orbit. In addition the orbit characterises a
resulting 'bubble' of chaos, itself a saddle, deep within the turbulent sea
(Kreilos et al. 2014). We explicitly analyse the merger of the two saddles and
show how it results in a considerable increase of the total lifetime. Both
exits and entries to the bubble are observed, as the stable manifolds of the
inner and outer saddles intertwine. We observe that the typical lifetime of the
turbulence is influenced by switches between the inner and outer saddles, and
is thereby dependent on whether or not it 'shadows' or 'visits' the vicinity of
the long-period RPO (Cvitanovic et al. 2014). These observations, along with
comparisons of flow structures, show that RPOs play a significant role in
structuring the dynamics of turbulence.

18
The categories of this paper are: econ
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org