Z^d在紧拓扑群上的平移作用

Z^d action on compact groups by rotation.

利用Markov-Kakutani不动点定理证明了紧群上的Zd左平移作用是拓扑可迁的当且仅当是遍历的.该结论推广了Z作用时相应的结论,而且证明方法是初等的.

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.