EXERCISE 3: [20 points- 5 points each part] A dynamical system f : C ? C is defined by 3: if Re(-) ? 0.5 2z - 1 if Re(z) 2 0.5 (i) Identify the set of points A C C whose orbits do not leave the closed ball B(0,2). (ii) Identify the basin of attraction of "the point at infin- ity''. (iii) Identify the set of points-E?0, 1| such that(/) , fo2?? c 10, 11 ad such that fo3() 1 that takes exactly 212 iterations to leave ?, 11 0,1. (iv) Find a point, very close to A, EXERCISE 3: [20 points- 5 points each part] A dynamical system f : C ? C is defined by 3: if Re(-) ? 0.5 2z - 1 if Re(z) 2 0.5 (i) Identify the set of points A C C whose orbits do not leave the closed ball B(0,2). (ii) Identify the basin of attraction of "the point at infin- ity''. (iii) Identify the set of points-E?0, 1| such that(/) , fo2?? c 10, 11 ad such that fo3() 1 that takes exactly 212 iterations to leave ?, 11 0,1. (iv) Find a point, very close to A