In this lecture I will introduce the dynamical quantities able to measure the (information-theoretic) “complexity” of
a dynamical system, namely the entropies associated with that system.
These entropies are of two types: a Kolmogorov-Sinai entropy is associated with each invariant probability measure, and
quantifies the complexity with respect to that measure. On the other hand, the
topological entropy is merely defined in terms of the map (or flow) independently of any
underlying measure; in some cases, it provides informations on the number of long periodic orbits.
A variational principle connects the two versions.

IPhT