RE: Simple Recursive Map
- To: mathgroup at smc.vnet.net
- Subject: [mg35436] RE: [mg35398] Simple Recursive Map
- From: "DrBob" <majort at cox-internet.com>
- Date: Fri, 12 Jul 2002 04:28:58 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
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