Persistence of the Feigenbaum attractor in one-parameter families

被引:3
|
作者
Catsigeras, E [1 ]
Enrich, H [1 ]
机构
[1] IMERL, Fac Ingn, Montevideo, Uruguay
关键词
D O I
10.1007/s002200050739
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Consider a map psi(0) of class C-r for large r of a manifold of dimension n greater than of equal to 2 having a Feigenbaum attractor. We prove that any such psi(0) 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 psi(0). We also construct such a transversal family for any given psi(0), and apply this construction to prove a conjecture by J. palls stating that a map exhibiting a Feigenbaum attractor can be perturbed to obtain homoclinic tangencies.
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页码:621 / 640
页数:20
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