动力系统的遍历性

Ergodicity of dynamical systems

给出遍历性及唯一遍历的几个等价条件。主要结果是定理4、定理6及定理7.并利用定理4给出定理5的一个证明。定理6及定理7给出唯一遍历的等价条件,定理7的证明采用的是泛函分析的方法。

The purpose of this article is to give some equivalent conditions for ergodicity and unique ergodicity. The main results are sheorem 4, theorem 6 and theorem 7. Theorem 4 gives asufficient and nassary condition for ergodicity, and we give a proof of theorem 5 by theorem 4. Some equivalent conditions for unique ergodicity are included in theorem 6 and theorem 7 and the methods of the proof of theorem 7 is from functional analysis.