一类CA的遍历理论

Ergodic Theory of a Class of CA

一类特殊ＣＡ的遍历理论。主要结果有：关于这类ＣＡ的Ｒｕｅｌｅ＇ｓＰｅｒｒｏｎＦｒｏｂｅｎｉｕｓ定理；Ｇｉｂｂｓ测度的存在性；

Let D rb ={ f∈C(Σ b,Σ b):f is generated by a block map of rank r which is permutation at position 1 and (2r+1)} and F= {φ∈C(Σ b) : for some b>0 and α∈(0,1) , var k φbα k, k0} . For any τ∈D rb and φ∈F , we obtain the following results: 1) Ruelle's Perron Frobenius theorem, 2) there is unique Gibbs state, 3) there is unique equilibrium state.