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We've al ready worked out how to find equations for the fixed points and two-cy cles. What about other cycles?" }}{PARA 3 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "F := x -> x^2 + c;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&*$)9$\"\"#\"\"\"F1%\"cGF1F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 13 "Fixed points:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "fi xed := implicitplot(F(x)=x, c=-2..0.5, x=-2..4, numpoints=1000, thick ness=2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(fixed); " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%'CURVESG6[ s7$7$$!\"#\"\"!$!3J\\\">`D/M(**!#=7$$!3zUr&G9d`&>!#<$!3&4dG9dG9#)*F-7$ 7$$!3+++++](=#>F1$!3,Q1^3oW2(*F-F.7$7$F($\"3kO=fz*[u*>F17$$!3r.&o>D%[Q >F1$\"3\\4Ws/AOx>F17$7$F6$\"3D/-^v(Q>(>F1F>7$F57$$!3MU7!=6Pp)=F1$!3C'= 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0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "What, you ask, about the poor 5-cycles? Unfortunately, \+ Maple cannot find them, since Maple is unable to factor " }{XPPEDIT 18 0 "(`@@`(F,5)(x)-x)/(F(x)-x);" "6#*&,&--%#@@G6$%\"FG\"\"&6#%\"xG\" \"\"F,!\"\"F-,&-F)6#F,F-F,F.F." }{TEXT -1 13 ". 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