# Question:Evaluating Lyapunov exponent

## Question:Evaluating Lyapunov exponent

Hi! this is another question about chaos dynamic in Maple last question was about invariant denisty measure on which user Carl Love helped me to answer. Below is link to this question:

https://www.mapleprimes.com/questions/233277-How-To-Optimize-Code-For-Counting-Experimental

So now I want to sketch Lyapunov exponent:

restart;
with(plots);
M := 100;
r := evalf([seq(a/M, a = 3*M .. 4*M)]);
x := t -> t;
x0 := 0.2;
iter := 8;

f := x -> r[i]*x*(1 - x)

g := (n, x) -> (f@@n)(x)

L := seq(D(g(iter, x))(x0), i = 1 .. M)

lambda := seq(ln(abs(L[i]))/iter, i = 1 .. M)

pointplot([seq([3 + a/M, lambda[a]], a = 1 .. M)])

here for comparison a better assignment

main problem is to take proper M and iter because iter above 8 takes too much time to calculate and M additonaly extends the time of calculations. M here is about dividing domain of our function lambda and higher M means more accurate value. Iter is from definition of Lyapunov exponent lambda(x0)=lim  1/{iter}( ln(|diff(f^{iter}(x0),x)| ),iter goes to infinity). Iter is for the more irregular shape of the curve.

Thanks in advance and Merry Christmas.

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