Problem 2: Consider the shift o on the space E (3 symbols, say {1, 2, 3 }). a) Find the fixed points and all points of period 2; b) Find the the number of periodic points of periods 1,2,3,4,5,6; c) Estimate the number of periodic points of period k for large k and find the limit limk- - log(#Perk(o) ), where Perk(o) is the set of period k points of o; d) Let p = (1, 1, 1, 1, ...) be a fixed point of o. Construct a point T E E, , such that trajectory of x comes arbitrarily close to p but never does hit p exactly; d) Let p1 = (1, 1, 1, 1, ...) and p2 = (2, 2, 2, 2, . ..) be two fixed points of o. Construct a point T E Z3 , such that trajectory of x comes arbitrarily close to both p1 and p2