arXiv math/94012251994-01-29math.DS

Absorbing Cantor sets in dynamical systems: Fibonacci maps

Henk Bruin, Gerhard Keller, Tomasz Nowicki, Sebastian van Strien

英文摘要：

In this paper we shall show that there exists a polynomial unimodal map f: [0,1] -> [0,1] which is 1) non-renormalizable(therefore for each x from a residual set, $ω(x)$ is equal to an interval), 2) for which $ω(c)$ is a Cantor set, and 3) for which $ω(x)=ω(c)$ for Lebesgue almost all x. So the topological and the metric attractor of such a map do not coincide. This gives the answer to a question posed by Milnor.

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