  In this article we prove two formulas for the topological entropy of an
F-optical Hamiltonian flow induced by a C^{\infty} Hamiltonian, where F is a
Lagrangian distribution. In these formulas, we calculate the topological
entropy as the exponential growth rate of the average of the determinant of the
differential of the flow, restricted to the Lagrangian distribution or to a
proper modification.
