  Spatial diffusion of particles in periodic potential models has provided a
good framework for studying the role of chaos in global properties of classical
systems. Here a bidimensional "soft" billiard, classically modeled from an
optical lattice hamiltonian system, is used to study diffusion transitions with
the control parameters variation. Sudden transitions between normal and
ballistic regimes are found and characterized by inspection of the topological
changes in phase-space. Transitions correlated with increases in global
stability area are shown to occur for energy levels where local maxima points
become accessible, deviating trajectories approaching it. These instabilities
promote a slowing down of the dynamics and an island myriad bifurcation
phenomenon, along with the suppression of long flights within the lattice.
Other diffusion regime variations occurring during small intervals of control
parameters are shown to be related to the emergence of a set of orbits with
long flights, thus altering the total average displacement for long integration
times but without global changes in phase-space.
