a) Let f: S^1 -> S^1 be conjugated to an irratonal rotation. Show that the congujacy is unique up to rotation, i.e, if h1 and h2 are two conjugacies then h1 = R_alpha o h2, for some alpha.

b)Show that tere are no expansive homeomorphism in S^1 (Hint: consider the rational, and irrational rotation number cases separately).


Thank you!