Absorbing Cantor sets in dynamical systems: Fibonacci maps
Dynamical Systems
2008-02-03 v1
Abstract
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, is equal to an interval), 2) for which is a Cantor set, and 3) for which 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.
Cite
@article{arxiv.math/9401225,
title = {Absorbing Cantor sets in dynamical systems: Fibonacci maps},
author = {Henk Bruin and Gerhard Keller and Tomasz Nowicki and Sebastian van Strien},
journal= {arXiv preprint arXiv:math/9401225},
year = {2008}
}