Prove that a homeomorphism of R cannot have periodic points with prime period greater than 2. Give an example of a homeomorphism that has a point of prime period 2. Show that the tripling map  (mod 1)...

Prove that a homeomorphism of R cannot have periodic points with prime period greater than 2. Give an example of a homeomorphism that has a point of prime period 2.

Show that the tripling map
 (mod 1) is topologically transitive and the set of periodic points Perf is dense in [0, 1] (use a ternary expansion).