defining function on mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg22273] defining function on mathematica*From*: Elisha Kobre <ekobre at erols.com>*Date*: Mon, 21 Feb 2000 20:00:41 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Could someone PLEASE help with the following mathematica progrmming problem: I have a family of functions indexed by w where w lies in the interval [0,1). The functions are f[x_]:= x+ w +1/1000 Sin[2 Pi x]. I want to define (AND PLOT) a function h[w] where for each value of w, h[w] is the 1000th iterate of f (with the specific w inserted into f) on x=0 ,divided by 1000 ---(this is supposed to approximate the so called rotation number). The graph of h[w] is called a devils staircase. How can we define h so it works and we get a good plot ? I have tried nest, fold etc.... but run into problems with all of them. I'll Be glad to provide more details. Thanks Elisha Kobre