## Institute for Mathematical Sciences

## Preprint ims94-2

** H. Bruin, G. Keller, T. Nowicki, & S. van Strien**
* Absorbing Cantor sets in dynamical systems: Fibonacci maps*

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, $\omega(x)$ is equal to an interval),
2) for which $\omega(c)$ is a Cantor set, and
3) for which $\omega(x)=\omega(c)$ 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.

View ims94-2 (PDF format)