1994/01/29 by Henk Bruin, Bruin, Henk, Gerhard Keller +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.math/9401225
openalex publication_date 1994/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.