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MathGroup Archive 2002

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Re: Simple Recursive Map

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35428] Re: [mg35398] Simple Recursive Map
  • From: Hugh Walker <hwalker at gvtc.com>
  • Date: Fri, 12 Jul 2002 04:28:43 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On Thursday, July 11, 2002, at 04:24 AM, Reuben wrote:

> 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

I think this is what you want.

x[n_] := y[n - 1] - a*x[n - 1]^2 - 1
y[n_] := b*x[n - 1]
{a, b, x[0], y[0]} = {1, 1, 1, 1};

The first few results are

Table[{x[k], y[k]}, {k, 7}]

{{-1, 1}, {-1, -1}, {-3, -1}, {-11, -3}, {-125, -11},
   {-15637, -125}, {-244515895, -15637}}

============
   Hugh Walker
    Gnarly Oaks



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