摘要
证明了在紧致T2 空间中 ,一个具有正拓扑熵的流 (X ,T)必含有熵对 ,(X ,T)的熵对的全体是X×X的T×T -不变的集合 .而且 ,若π :(Y ,S) → (X ,T)为因子映射 ,(x,x′)为 (X ,T)的熵对 ,那么 (x ,x′)的逆像中含有 (Y ,S)的熵对 ;反之 ,若(y,y′)为 (Y ,S)的熵对 ,并且π(y) ≠π(y′) ,则 (π(y) ,π(y′) )为 (X ,T)的熵对 .进而利用熵对的这个性质可以说明极小零拓扑熵流与对角流的不交性以及流的极大零熵因子的存在性 .上述结果推广了Blanchard等人关于紧致度量空间上流的相应性质 .
The results have been obtained as following: if ( X,T) is a compact Hausdorff flow with positive entropy, it must have entropy pairs and the collection of all entropy pairs of (X,T) is an T×T-inv ariant subset of X×X. Furthermore, if π:(Y,S)→(X,T) is a factor m ap and (x,x′) is an entropy pair of (X,T), then there is an entropy pair of (Y,S) in the fibre of (x,x′). On the other hand, if (y,y ′) is an entropy pair of (Y,S) and π(y)≠π(y′), then (π(y), π(y′)) is an entropy pair of (X,T). These properties can be used to sho w that minimal flows with zero entropy are disjoint from u.p.e. flows, and that a compact Hausdroff flow always has a maximal zero entropy factor. These result s are the generalizations of the corresponding properties of the flows on compac t metric spaces. An example is given to show that the separateness is necessary.
关键词
紧T2流
u.p.e.系统
熵对
极大零熵因子
不交性
compact Hausdorff flow
u.p.e. system
entrop y pair
maximal zero entropy factor
disjointness
