摘要
1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For every integer k≥2, define metrics d<sub>k</sub>and d<sub>k</sub>’ on X by d<sub>k</sub>（a,b）=max{k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>|: i=0, 1, 2,…}, d<sub>k</sub>’（a, b）=sum from i=0 to ∞ k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>| forany a=（a<sub>0</sub>, a<sub>0</sub>, a<sub>2</sub>,…） and any b=（b<sub>0</sub>, b<sub>1</sub>, b<sub>2</sub>,…）∈X. It is easy to see that all d<sub>k</sub> andd<sub>k</sub>’ induce the same topological structure. Thus we now may only consider d≡d<sub>2</sub>. Thespace （X, d） is usually called a symbolic space. For simplicity, write X for （X, d）. It
基金
Project supported by the National Natural Science Foundation of China.
