【摘要】 设(X,T)为拓扑动力系统,它的包络半群E(X,T)定义为 {Tn:n∈ Z+} 在 XX 中乘积拓扑下的闭包,如果元素u∈E(X,T)满足u2 = u,则称之为幂等元.本文研究包络半群仅含有限个幂等元的系统的性质,证明这类系统为 semi distal的,并且对照其他动力学性质,指出这类系统的动力学性状相对简单,并提供了许多例子进行论证.更多还原

【Abstract】 Let (X,T) be a topological dynamical system and its enveloping semigroup E(X,T) the closure of {T n:n∈Z +} in X X. An u∈E(X,T) with u 2=u is called an idempotent.The systems with enveloping semigroup containing finitely many idempotents are studied in this paper.It is shown that they are semi-distal.And comparing it with other dynamical properties we try to point out that the property we defined is not complex.Examples are given in the final section.更多还原