  The Scattered Disk Objects (SDOs) are thought to be a small fraction of the
ancient population of leftover planetesimals in the outer solar system that
were gravitationally scattered by the giant planets and have managed to survive
primarily by capture and sticking in Neptune's exterior mean motion resonances
(MMRs). In order to advance understanding of the role of MMRs in the dynamics
of the SDOs, we investigate the phase space structure of a large number of
Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincar\'e
sections of the circular planar restricted three body model for the full range
of particle eccentricity pertinent to SDOs. We find that, for eccentricities
corresponding to perihelion distances near Neptune's orbit, distant MMRs have
stable regions with widths that are surprisingly large and of similar size to
those of the closer-in MMRs. We identify a phase-shifted second resonance zone
that exists in the phase space at planet-crossing eccentricities but not at
lower eccentricities; this second resonance zone plays an important role in the
dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative
measurements of the sizes of the stable resonance zones confirm previous
results and provide an additional explanation for the prominence of the $N$:1
sequence of MMRs over the $N$:2, $N$:3 sequences and other MMRs in the
population statistics of SDOs; our results also provide a tool to more easily
identify resonant objects.
