Entropy of a skew product with a \(Z^ 2\)-action
This paper deals with the entropy of a skew product with a \(Z^2\) action generated by a cellular automaton (i.e., one of the generators of the \(Z^2\) action is generated by a block map). The cone entropy and the directional entropy are first proved to be the same for such a \(Z^2\) action. Then the author considers the entropy of a dynamical system generated by a skew product, where there is a \(Z^2\) action defined by a cellular automaton on the second fiber. In this case, the fiber contribution to the entropy is proved to be equal to the directional entropy in the direction of the integral of the skewing function, as expected from the classical case where \(Z\) acts on the two fibers.
scientific article; zbMATH DE number 910255