A thermodynamic formalism for one dimensional cellular automata (Q1293937)

The paper reviews results from the topological dynamics of one-dimensional cellular automata and gives a thermodynamical formalism for them. A one-dimensional cellular automaton is viewed as the topological dynamics on product space of a finite set of the natural numbers with a special local map. Since the transient dynamics show various phenomena the orbit structure is too complicated to treat with typical methods from dynamical systems. Instead the author uses the dynamical zeta function with a potential function and the structure matrix. As a result he gets a formula for the zeta function and as an illustration he gives examples for two different explicit local maps.