(4) Compute numerically the Lyapunov exponents for the logistic map at a=3.25. Demonstrate that the averages of the logs of the derivatives converge exponentially in this case and explain why. Compute the limit explicitly by finding the period-2 orbit as a solution to f(f(x)=x explicitly and evaluating derivatives along the orbit(you may use computational software to solve this equation or notice that you already know 2 solutions, the fixed points, to this fourth order equation explicitly, so the remaining ones solve a quadratic equation). Submit code as .m file (and whatever you are using to solve the fixed point equation, screenshot enough), and explain your steps and results. (4) Compute numerically the Lyapunov exponents for the logistic map at a=3.25. Demonstrate that the averages of the logs of the derivatives converge exponentially in this case and explain why. Compute the limit explicitly by finding the period-2 orbit as a solution to f(f(x)=x explicitly and evaluating derivatives along the orbit(you may use computational software to solve this equation or notice that you already know 2 solutions, the fixed points, to this fourth order equation explicitly, so the remaining ones solve a quadratic equation). Submit code as .m file (and whatever you are using to solve the fixed point equation, screenshot enough), and explain your steps and results