Algebraic topological entropy

Abstract

As a "by-product" of the Connes-Nainhofer-Thirring theory of dynamical entropy for (originally nonAbelian) nuclear C*-algebras, the well-known variational principle for topological entropy is equivalently reformulated in purely algebraically defined terms for (separable) Abelian C*-algebras. This "algebraic variational principle" should not only nicely illustrate the ''feed-back'' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by "algebraic" methods and could thus further simplify the original proof of the variational principle (at least "in principle"). Invited contribution to the International Seminar on Applied Mathematics (ISAM 90) on "Dynamical Systems", Gaussig, GDR.