Gleichgewichts- und Gibbs-Maße für zelluläre Automaten

Abstract

In this work two families of cellular automatas (CA) are studied as dynamical systems.The theory of fibre systems and relative pressure due to Walters will be of importancein order to answer crucial problems in ergodic theory for such automata. Indeed it is possible to calculate the topological entropy and to find an explicit measure ofmaximal entropy. Furthermore the exposed method allows to calculate the topological pressure and to give some equilibrium states for the considered systems and potentials.Finally some results about the existence and uniqueness of Gibbs measures are stated.It is to underline that the considered CA are defined over subshifts of finite type and that many results are stated in a more general case such that the proposed method can be helpful for the study of other systems.