From: Joseph Dale <jdale@uclink4.berkeley.edu>
Subject: Re: rx(1-x)
Date: Fri, 29 Oct 1999 21:02:32 GMT
Newsgroups: sci.math.research
Keywords: behaviour (periodic points) of logistic map for large coefficient r

daan wrote:
> 
> Hello,
> 
> has anybody by chance studied the logistic map:
> 
> h(x)=rx(1-x)
> 
> for r>3.57 ?
> 
> Like to hear from you!
> 
> Daan
> (remove BACH from address when replying)

I haven't myself, but here's a tidbit from "A First Course in Discrete
Dynamical Systems," by Richard Holmgren: "The entire period-doubling
cascade will have been completed by the time r=3.57 and there will be a
periodic point with prime period 2^n for each n whenever r>=3.57."

Holmgren points to further references on the behavior of the logistic
function in this range in works by Peitgen, Jurgens, and Saupe, and by
Devaney.