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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 18 "A Dynamical System" }
{TEXT -1 64 "\nIterration function(s) for an example from Math 436, Fa
ll 2003." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;\nwith(plots):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "g := x -> x - (x^2-5)/m
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(g(x)=x,x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "g1 := x -> x - (x^2-5):\ng2
 := x -> x - (x^2-5)/2:\ng3 := x -> x - (x^2-5)/5:\nplot([g1(x),g2(x),
g3(x),x],x=0..5,color=[red,blue,maroon,black],view = [0..5,0..5], scal
ing=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "Gr1 :
= animate(g(x),x=-10..10,m=0.2..12,view=[-10..10,-10..10],scaling=cons
trained,frames=200):\nGr2 := plot(x,x=-10..10,color=blue):\ndisplay(Gr
1,Gr2);" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "D(g)(x);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "solve(D(g)(sqrt(5)) < -
1,m);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "X := 2; X := g1(X)
; X := g1(X); X := g1(X); X := g1(X); X := g1(X);" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "X := 1.5; X
 := g2(X); X := g2(X); X := g2(X); X := g2(X); X := g2(X);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "G := x-> g(g(x));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "G(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "simplify(G(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "solve(G(x)=x,x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 251 "G1 := subs(m=1,G(x)): simplify(G1);\nG2 := subs(m=2,
G(x)): simplify(G2);\nG3 := subs(m=3,G(x)): simplify(G3);\nG5 := subs(
m=5,G(x)): simplify(G5);\nplot([G1,G2,G3,G5,x],x=0..5,color=[red,blue,
maroon,magenta,black],view = [0..5,0..5], scaling=constrained);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "Gr1 := animate(G(x),x=0..5,m=1..8,v
iew=[0..5,0..5],scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Gr2 := plot(x,x=0..5,color=blue):" }}}{EXCHG {PARA 0 
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