关键词: 符号动力系统, CA, Gibbs测度, 遍历

Abstract: 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_kφ<=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.

Key words: symbolic dynamical system, CA, Gibbs state, ergodicity