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arXiv · 0805.1152

The real analytic Feigenbaum-Coullet-Tresser attractor in the disk

E. Catsigeras·M. Cerminara·H. Enrich
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Abstract

We consider a real analytic diffeomorphism $ψ_0$ 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 $ϕ_0$ fixed by the double renormalization. We prove that $ψ_0$ 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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E. Catsigeras, M. Cerminara, H. Enrich. 2008-05-08. The real analytic Feigenbaum-Coullet-Tresser attractor in the disk. https://doi.org/10.1080/14689361003785727

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