(*  07/01  2.25 PM  *)
(*  This program will compare the even and odd iterations of the degree 6   *)(*  mapping.  Even iterations will be shown in purple, odd in green,   *)
(*  and then the two graphs will be overlaid  *)

(***   PART 1:  degree 6   ***)
Clear[AA,BB,CC,T,a,b,c,ans,evenans, oddans,i, G1,G2];
AA[{{a_, b_}, c_}] := (a*b + 5 a + 5 b + c)/((a + b + 2)^(4))^(1/3)
BB[{a_, b_}] := (a + b + 6)/((a + b + 2)^(2))^(1/3)
T[n_] := T[n] = {AA[{T[n - 1], CC}], BB[T[n - 1]]} // N
CC = 9.0;

(*** Enter Initial Conditions  ***)
T[1] = {-9.0,-4.2};
ans = Table[T[i],{i,1,100010}];
evenans = Table[ans[[i]], {i,2,100000,2}];
oddans = Table[ans[[i]],{i,1,100000,2}];

Print[AA[{{a,b},CC}]]
Print[ Initial Condition:  T[1]]
G1 = ListPlot[evenans, PlotStyle->{Hue[.8], PointSize[0.0005]} ,DisplayFunction ->Identity]
G2 = ListPlot[oddans,PlotStyle->{Hue[.6], PointSize[0.0005]},DisplayFunction->Identity ]
   Show[G1,G2,DisplayFunction->$DisplayFunction]