Z~d action on compact groups by rotation.
Enhui Shi · Journal of Zhejiang University(Sciences Edition) · 2004
By using the method of Markov-Kakutani fixed point theorem, it is proved that Z~d action on compact groups by rotation is topologically transitive if and only if it is ergodic. It is a generalization of the similar result of Z actions, and the method used in the proof is elementary.