1. Engineering
  2. Mechanical Engineering
  3. consider the following dynamical system state space 2n dynamical map...

Question: consider the following dynamical system state space 2n dynamical map...

Question details

Consider the following dynamical system State space: 2N. Dynamical map: Each 0 thats followed by a 0 turns into a 1, and each 1 thats followed by a 1 turns into a 0. Lets call this map E. As a demonstration, heres what E does to one point in 2 w 001110011011110000101110... E() 100010001000011110100010 a. Find two fixed points of E, and convince the grader theyre the only two. (Corrected. The previous version claimed, incorrectly, that there was only one fixed point.) b. Find two points with minimum period 2, and convince the grader theyre the only ones. HINT: You already know what E does to the first digit of each 2-digit block. Figure out what E2 does to the first digit of each 3-digit block. c. The two points with minimum period 2 form a 2-periodic orbit. Convince the grader that this orbit is repelling. HINT: To show that a 2-periodic orbit is repelling, you pick a point p on the orbit and show that its a repelling fixed point of E2. As a first step, consider a point w which first differs from p at the (n 1)st digit, and see what E2 does to the first n digits of w.
Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution