Abstract

this paper I discuss a number of "entropies" which have definitions which are respectively probabilistic, topological, algebraic, and algorithmic. I shall explain how these entropies are all defined in the setting of shift dynamical systems. The main result of the paper, which should be regarded as part of the folklore, is the fact that for topologically transitive shifts of finite type (the definitions of these terms will be found below) all these entropies agree numerically.

Citations