Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Center problem, Abel equation and the Faa di Bruno Hopf algebra for
  output feedback   A combinatorial interpretation is given of Devlin's word problem underlying
the classical center-focus problem of Poincare for non-autonomous differential
equations. It turns out that the canonical polynomials of Devlin are from the
point of view of connected graded Hopf algebras intimately related to the
graded components of a Hopf algebra antipode applied to the formal power series
of Ferfera. The link is made by passing through control theory since the Abel
equation, which describes a center, is equivalent to an output feedback
equation, and the Hopf algebra of output feedback is derived from the
composition of iterated integrals rather than just the products of iterated
integrals, which yields the shuffle algebra. This means that the primary
algebraic structure at play in Devlin's approach is actually not the shuffle
algebra, but a Faa di Bruno type Hopf algebra, which is defined in terms of the
shuffle product but is a distinct algebraic structure.

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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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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: cs
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The categories of this paper are: nucl-ex