Editorial Addresses

We study the existence and structure of extremals for one-dimensional variational problems on a torus and the properties of the minimal average action as a function of the rotation number. We show that, for a generic integrand f, the minimum of the minimal average action is attained at a rational point mn ^–1 where n1 and m are integers; also, for each initial value, there exists an (f)-weakly optimal solution over an infinite horizon.