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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