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MathGroup Archive 2002

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Re: Simple Recursive Map

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35437] Re: [mg35398] Simple Recursive Map
  • From: Tomas Garza <tgarza01 at prodigy.net.mx>
  • Date: Fri, 12 Jul 2002 04:29:00 -0400 (EDT)
  • References: <200207110924.FAA02123@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

To start with, you must use the proper syntax, and then set up a recursion.
You have not given initial values, so I arbitrarily set x[1] = 1 and y[1] =
0. Then

In[1]:=
x[n_] := y[n - 1] - a*x[n - 1]^2 - 1;
y[n_] := b + x[n - 1];
x[1] := 1;
y[1] := 0;

recursion limit (q.v.), usually equal to 256 by default. Bear in mind that
you are getting very complicated expressions as n grows larger, if a and b
remain in symbolic form, and the execution time may also be quite large.
Take, for example, n = 10:

In[2]:=
Timing[Collect[y[10], {a, b}]; ]
Out[2]=
{118.2 Second, Null}

I used Collect to obtain a neater result. Of course, I didn't display it.

Tomas Garza
Mexico City
----- Original Message -----
From: "Reuben" <reubengann at hotmail.com>
To: mathgroup at smc.vnet.net
Subject: [mg35437] [mg35398] Simple Recursive Map


> I have the map
>
> x_n+1=y_n-a*(x_n)^2 - 1
> y_n+1=b*x_n
>
> If I specify a,b, x_0 and y_0, how can I make Mathematica iterate
> through this numerically to give me x_50 and y_50?
>
> Thanks
> Reuben
>



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