Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Marden theorem and Poncelet-Darboux curves   The Marden theorem of geometry of polynomials and the great Poncelet theorem
from projective geometry of conics by their classical beauty occupy very
special places. Our main aim is to present a strong and unexpected relationship
between the two theorems. We establish a dynamical equivalence between the full
Marden theorem and the Poncelet-Darboux theorem. By introducing a class of {\it
isofocal deformations}, we construct morphisms between the Marden curves and
the Poncelet-Darboux curves. Then we present effective criterion in terms of
pair of polynomials which defines a Poncelet-Darboux curve of degree $n-1$, for
complete decomposition of the curve on $(n-1)/2$ conics if $n$ is odd; if $n$
is even, complete decomposition consists of $(n-2)/2$ conics and a line. This
is an important question in the study of special, 'tHooft, instanton bundles.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph