We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.
We investigate topological entropy of periodic Coven cellular automatas; that is, the maps Fs： （0, 1）^z → {0, 1）^z defined by FB（x）i=xi＋^rПj=1（xi＋j＋bj）（mod 2）, where B = b1b2…br ∈ {0, 1}^r（r≥2）, is a periodic word. In particular, we prove that if the minimal period of B is greater than 5, the topological entropy is log 2.
