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 >

**References**:**Simple Recursive Map***From:*Reuben <reubengann@hotmail.com>