(a): Find a scheme to provide for any positive integer n, a sequence S1 ...Sn+1 of the symbols L and R such that S1 = Sn+1, and such that the sequence S1 ...Sn is not the juxtaposition of identical subsequences of shorter length. For example, the sequence LRLRL does NOT guarantee the existence of a period-4 orbit; the sequence LRRLL does.

(b): Prove that the logistic map G has a periodic orbit for each integer period.

PLEASE ANSWER BOTH PARTS // THANK YOU VERY MUCH

3. (a): Find a scheme to provide for any positive integer n, a sequence Si. . . Sn+1 of the symbols L and R such that S,-Sn+1, and such that the sequence Si . ..Sn is not the juxtaposition of identical subsequences of shorter length. For example, the sequence LRLRL does NOT guarantee the existence of a period-4 orbit; the sequence LRRLL does. (b): Prove that the logistic map G has a periodic orbit for each integer period. 3. (a): Find a scheme to provide for any positive integer n, a sequence Si. . . Sn+1 of the symbols L and R such that S,-Sn+1, and such that the sequence Si . ..Sn is not the juxtaposition of identical subsequences of shorter length. For example, the sequence LRLRL does NOT guarantee the existence of a period-4 orbit; the sequence LRRLL does. (b): Prove that the logistic map G has a periodic orbit for each integer period