We begin this lecture by defining a generator of a dynamical system, and a weak generator of a reversible dynamical system. We then prove that a dynamical system is (weakly) expansive if and only if it admits a (weak) generator.

Motivated by this, we study open covers in general. We define the entropy of an open cover to be the logarithm of the cardinality of a minimal subcover, and use this to give a new definition of topological entropy in terms of open covers.

Comments and questions?