Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The moduli space of germs of generic families of analytic
  diffeomorphisms unfolding a parabolic fixed point   In this paper we describe the moduli space of germs of generic families of
analytic diffeomorphisms which unfold a parabolic fixed point of codimension 1.
  In [MRR] (and also [R]), it was shown that the Ecalle-Voronin modulus can be
unfolded to give a complete modulus for such germs. The modulus is defined on a
ramified sector in the canonical perturbation parameter $\eps$. As in the case
of the Ecalle-Voronin modulus, the modulus is defined up to a linear scaling
depending only on $\eps$.
  Here, we characterize the moduli space for such unfoldings by finding the
compatibility conditions on the modulus which are necessary and sufficient for
realization as the modulus of an unfolding.
  The compatibility condition is obtained by considering the region of
sectorial overlap in $\eps$-space. This lies in the Glutsyuk sector where the
two fixed points are hyperbolic and connected by the orbits of the
diffeomorphism. In this region we have two representatives of the modulus which
describe the same dynamics. We identify the necessary compatibility condition
between these two representatives by comparing them both with their common
Glutsyuk modulus.
  The compatibility condition implies the existence of a linear scaling for
which the modulus is 1/2-summable in $\eps$, whose direction of non-summability
coincides with the direction of real multipliers at the fixed points.
Conversely, we show that the compatibility condition (which implies the
summability property) is sufficient to realize the modulus as coming from an
analytic unfolding, thus giving a complete description of the space of moduli.

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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: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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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: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat