半群作用的传递属性

The transitivity of semigroup action

研究了半群作用的传递属性.证明了一个系统是thick传递的当且仅当它是弱混合的,其中作用半群是一个交换的幺半群;此外,还证明了一个几乎周期点稠密的(△syndetic)*传递系统是弱混合的,其中作用半群是一个交换半群.

This paper deals with the transitivity of semigroup action.We show that a system is thick transitive if it is weakly mixing,where the semigroup which acts on the space is an abelian monoid.Additionally,we show that a（△syndetic）＊ transitive system with dense almost period points is weakly mixing,where the semigroup which acts on the space is an abelian semigroup.