  In this work we analyze the bifurcation of dividing surfaces that occurs as a
result of a pitchfork bifurcation of periodic orbits in a two degrees of
freedom Hamiltonian System. The potential energy surface of the system that we
consider has four critical points: two minima, a high energy saddle and a lower
energy saddle separating two wells (minima). In this paper we study the
structure, the range, and the minimum and maximum extent of the periodic orbit
dividing surfaces of the family of periodic orbits of the lower saddle as a
function of the total energy.
