  We introduce a new measure of instability of area-preserving twist
diffeomorphisms, which generalizes the notions of angle of splitting of
separatrices, and flux through a gap of a Cantori. As an example of
application, we establish a sharp >0 lower bound on the topological entropy in
a neighbourhood of a hyperbolic, unique action-minimizing fixed point, assuming
only no topological obstruction to diffusion, i.e. no homotopically non-trivial
invariant circle consisting of orbits with the rotation number 0. The proof is
based on a new method of precise construction of positive entropy invariant
measures, applicable to more general Lagrangian systems, also in higher degrees
of freedom.
