无限型符号动力系统的一个几何解释

A GEOMETRIC INTERPRETATION OF INFINITE SYMBOLIC DYNAMICAL SYSTEMS

可列无穷个符号的符号序列空间Σ∞与区间Ｉ＝［０，ｌ］上的所有无理数构成的子空间Ｗ同胚，而Σ∞上的位移映射σ则与Ｗ上的高斯映射ｇ拓扑共轭．

Let Σ ∞be the space of onesided infinite sequence on infinite many symbols{0,1,2,…},and σ the shift map on Σ ∞.Let g be the Gauss map of the interval I= and w the set of irrationals in I.Then g is not continuous,but g|w is continuous and is topologically conjugate to σ.