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RE: Simple Recursive Map


You can use subscripts:

Subscript[x, 0] = 0
Subscript[y, 0] = 0
Subscript[x, n_] := Subscript[x, n] = 
   Expand[Subscript[y, n - 1] - 
     a*Subscript[x, n - 1]^2 - 1]
Subscript[y, n_] := Expand[b*Subscript[x, n - 1]]
Subscript[x, 5]

The function equivalent is much faster:

ClearAll[f, g]
f[0] = 0;
g[0] = 0;
f[n_] := f[n] = Expand[g[n - 1] - 
     a*f[n - 1]^2 - 1]
g[n_] := Expand[b f[n - 1]]

The fiftieth terms are a lost cause, until you give a and b specific
numerical values:

LeafCount@f@# & /@ Range[8]
Depth@f@# & /@ Range[8]

{1, 5, 18, 66, 271, 1091, 4376, 17500}
{1, 3, 4, 4, 4, 4, 4, 4}

Bobby

-----Original Message-----
From: Reuben [mailto:reubengann at hotmail.com] 
To: mathgroup at smc.vnet.net
Subject: [mg35436] [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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