The Lie-Trotter formula for strongly continuous semigroups of operators
in Banach spaces provides conditions such that switching between two
deterministic systems (represented by two of those semigroups) results
into new combined dynamics (i.e. a new semigroup) in the limit of
infinitely fast switching. We discuss the history of the formula and
exhibit then recently obtained results that apply to switching of Markov
semigroups, which correspond to Markov processes in continuous time.