Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A dynamical systems approach to a thin accretion disc and its
  time-dependent behaviour on large length scales   Modelling the flow in a thin accretion disc like a dynamical system, we
analyse the nature of the critical points of the steady solutions of the flow.
For the simple inviscid disc there are two critical points, with the outer one
being a saddle point and the inner one a centre type point. For the weakly
viscous disc, there are four possible critical points, of which the outermost
is a saddle point, while the next inner one is a spiral. Coupling the nature of
the critical points with the outer boundary condition of the flow, gives us a
complete understanding of all the important physical features of the flow
solutions in the subsonic regions of the disc. In the inviscid disc, the
physical realisability of the transonic solution passing through the saddle
point is addressed by considering a temporal evolution of the flow, which is a
very likely non-perturbative mechanism for selecting the transonic inflow
solution from among a host of other possible stable solutions. For the weakly
viscous disc, while a linearised time-dependent perturbation imposed on the
steady mass inflow rate causes instability, the same perturbative analysis
reveals that for the inviscid disc, there is a very close correspondence
between the equation for the propagation of the perturbation and the metric of
an acoustic black hole. Compatible with the transport of angular momentum to
the outer regions of the disc, a viscosity-limited length scale is defined for
the spatial extent of the inward rotational drift of matter.

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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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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: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat