Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The real analytic Feigenbaum-Coullet-Tresser attractor in the disk   We consider a real analytic diffeomorphism $\psi_0$ on a n-dimensional disk
D, n >= 2, exhibiting a Feigenbaum-Coullet-Tresser (F.C.T.) attractor, being
far, in the standard topology of the real analytic diffeomorphism space C(D),
from the standard F.C.T. map $\phi_0$ fixed by the double renormalization. We
prove that $\psi_0$ persists along a codimension-one manifold M \subset C(D),
and that it is the bifurcating map along any one-parameter family in $C(D)$
transversal to M, from diffeomorphisms attracted to sinks, to those which
exhibit chaos. The main tool in the proofs is a theorem of Functional Analysis,
which we state and prove in this paper, characterizing the existence of
codimension one submanifolds in any abstract functional Banach space.

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The categories of this paper are: eess
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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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: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: bayes-an