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Suppose I have the following function g[{x_, y_}, c0_, b_] := {x^2 + c0 - b*y, x} where b and c0 are parameter values.

Suppose we fix the values of c0 and b, say, g[{x_, y_}, -5, 1.2]. Is there a way to get the $nth$ composition of g with itself? So a function say G[{x_,y_},n,-5,1.2] which gives g[{x, y}, -5, 1.2] @* g[{x, y}, -5, 1.2] @* ... @* g[{x, y}, -5, 1.2] $n$ times? I would like to then use this to find period $n$ points using NSolve so I think this is the form I would require.

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2 Answers 2

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You can do something like:

gcomp[n_Integer] := Composition @@ ConstantArray[g[#, -5, 1.2] &, n]

Which you can then use as:

gcomp[3][{0, 0}]

Or perhaps even better:

gcomp[n_Integer, c0_, b_] := Composition @@ ConstantArray[g[#, c0, b] &, n];
gcomp[3, -5, 1.2][{0, 0}]
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  • $\begingroup$ This is wonderful thanks! $\endgroup$
    – math
    Nov 17, 2020 at 12:07
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n=3;
g[{x_, y_}, c0_, b_] := {x^2 + c0 - b*y, x};
Nest[Function[t, g[t, -5, 1.2]], {x0, y0}, n]
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  • $\begingroup$ n = 3; g[{x_, y_}, c0_, b_] := {x^2 + c0 - b*y, x}; Nest[g[#, -5, 1.2] &, {x0, y0}, n] $\endgroup$
    – cvgmt
    Nov 17, 2020 at 12:00

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