(a) Construct a continuous map that has a point of period 2 × 3, but no points of odd periods. (b) Describe the procedure of constructing a map of period 2n ×3, but has no points of period 2n−1× odd...

(a) Construct a continuous map that has a point of period 2 × 3, but no points of odd periods.

(b) Describe the procedure of constructing a map of period 2n ×3, but has no points of period 2n−1× odd integer.

For another construction of the double map on the same interval: Let I = [0, 1] and f : I → I be continuous. Define the double map ˜f by