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Question: Composition of mappimngs

Question:Composition of mappimngs

Gonzalo Garcia 155 Maple 17
procedure composition operator
June 12 2021
3

Hi!

Assume we have the following mappings:

 

f[1] := proc (x) options operator, arrow; piecewise(0 <= t and t <= 1/2, (1/2)*x(2*t), 1/2 < t and t <= 1, (1/2)*x(2*t-1)+1/2) end proc

 

f[2] := proc (x) options operator, arrow; t*x(t) end proc

 

 Note that the argument are mappings (i.e, x(t) is a continuous function defined on [0,1]). Given an array with values in {1,2}, for instance [1,1,2],and a function h (say, h:=t->t) How can we define the composition mapping f[1]f[1]f[2](h)?

In general, I want to plot the composition mapping f[i1]f[i2]...f[iN](h), i1,i2,...,iN being 1 or 2 and h a given continuous function defined on [0,1]

 

Many thanks in advance for your comments.

 

 
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