Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial models for spaces of cubic polynomials   A model for the Mandelbrot set is due to Thurston and is stated in the
language of geodesic laminations. The conjecture that the Mandelbrot set is
actually homeomorphic to this model is equivalent to the celebrated MLC
conjecture stating that the Mandelbrot set is locally connected. For parameter
spaces of higher degree polynomials, even conjectural models are missing, one
possible reason being that the higher degree analog of the MLC conjecture is
known to be false. We provide a combinatorial model for an essential part of
the parameter space of complex cubic polynomials, namely, for the space of all
cubic polynomials with connected Julia sets all of whose cycles are repelling
(we call such polynomials \emph{dendritic}). The description of the model turns
out to be very similar to that of Thurston.

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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex