  We study two related invariants of Lagrangian submanifolds in symplectic
manifolds. For a Lagrangian torus these invariants are functions on the first
cohomology of the torus. The first invariant is of topological nature and is
related to the study of Lagrangian isotopies with a given Lagrangian flux. More
specifically, it measures the length of straight paths in the first cohomology
that can be realized as the Lagrangian flux of a Lagrangian isotopy. The second
invariant is of analytical nature and comes from symplectic function theory. It
is defined for Lagrangian submanifolds admitting fibrations over a circle and
has a dynamical interpretation. We partially compute these invariants for
certain Lagrangian tori.
