Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A priori bounds for some infinitely renormalizable quadratics: III.
  Molecules   In this paper we prove {\it a priori bounds} for infinitely renormalizable
quadratic polynomials satisfying a ``molecule condition''. Roughly speaking,
this condition ensures that the renormalization combinatorics stay away from
the satellite types. These {\it a priori bounds} imply local connectivity of
the corresponding Julia sets and the Mandelbrot set at the corresponding
parameter values.

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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: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int