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Re: finding a symplectic recursion fixed point


This method has to be the hard way:
Clear[x, y, z, n, digits, a, b, s, g, a0]
(* SP(2) 3d  map*)
digits = 50;
x[n_] := x[n] = -Log[Exp[y[n - 1] + z[n - 1]] + 1]
y[n_] := y[n] = y[n - 1]*Log[2*Cosh[x[n - 1]]]
z[n_] := z[n] = z[n - 1]*Log[2*Cosh[x[n - 1]]]
x[0] := -0.69; y[0] := -0.001; z[0] := -0.001;
a = Table[Point[N[{Re[x[n]], Re[y[n]], Re[z[n]]}]], {n, 0, digits}]
Show[Graphics3D[a]]

One Fixed point is:
{-Log[2],0,0}



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