8. Consider the dynamical system xn+1 = = f (xn) = 3xn - x [1, 1]. a. Find an explicit formula for x using a trigonometric change of variables. (Hint: think about sin(3y) ...) b. Using a., show that the above dynamical system is equivalent (topologically conjugate) to the action of the chopping map on the ternary sequences .0121110122200021010001120122... c. Explain which trajectories of the chopping map are periodic and find the number of the p-periodic points and trajectories for any p. What are the corresponding periodic trajectories of the map ? d. Show that the chopping map (and hence the map f) is sensitive with respect to initial data. e*. Show that the chopping map is chaotic (e* is a bonus question).