The real analytic Feigenbaum-Coullet-Tresser attractor in the disk
نویسندگان
چکیده
We consider a real analytic diffeomorphism ψ0 on a n-dimensional disk D, n ≥ 2, exhibiting a Feigenbaum-Coullet-Trésser (F.C.T.) attractor, being far, in the Cω(D) topology, from the standard F.C.T. map φ0 fixed by the double renormalization. We prove that ψ0 persists along a codimension-one manifold M ⊂ Cω(D), and that it is the bifurcating map along any one-parameter family in Cω(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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