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Persistence of the Feigenbaum Attractor in One-Parameter Families

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Consider a map ψ0 of class C r for large r of a manifold of dimension n greater than or equal to 2 having a Feigenbaum attractor. We prove that any such ψ0 is a point of a local codimension-one manifold of C r transformations also exhibiting Feigenbaum attractors. In particular, the attractor persists when perturbing a one-parameter family transversal to that manifold at ψ0. We also construct such a transversal family for any given ψ0, and apply this construction to prove a conjecture by J. Palis stating that a map exhibiting a Feigenbaum attractor can be perturbed to obtain homoclinic tangencies.

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Received: 4 August 1998 / Accepted: 11 May 1999

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Catsigeras, E., Enrich, H. Persistence of the Feigenbaum Attractor in One-Parameter Families. Comm Math Phys 207, 621–640 (1999). https://doi.org/10.1007/s002200050739

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  • DOI: https://doi.org/10.1007/s002200050739

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