  Observations of Kuiper belt objects (KBOs) in Neptune's 5:2 resonance present
two puzzles: this third order resonance hosts a surprisingly large population,
comparable to the prominent populations of Plutinos and Twotinos in the first
order 3:2 and 2:1 resonances, respectively; secondly, their eccentricities are
concentrated near $0.4$. To shed light on these puzzles, we investigate the
phase space near this resonance with use of Poincar\'e sections of the circular
planar restricted three body model. We find several transitions in the phase
space structure with increasing eccentricity, which we explain with the
properties of the resonant orbit relative to Neptune's. The resonance width is
narrow for very small eccentricities, but widens dramatically for
$e\gtrsim0.2$, reaching a maximum near $e\approx0.4$, where it is similar to
the maximum widths of the 2:1 and 3:2 resonances. We confirm these results with
N-body numerical simulations, including the effects of all four giant planets
and a wide range of orbital inclinations of the KBOs. We find that the
boundaries of the stable resonance zone are not strongly sensitive to
inclination and remain very similar to those found with the simplified three
body model, with the caveat that orbits of eccentricity above $\sim0.53$ are
unstable; higher eccentricity orbits are phase-protected from destabilizing
encounters with Neptune but not with Uranus. These results show that the 5:2
resonant KBOs are not more puzzling than the Plutinos and Twotinos; however,
detailed understanding of the origins of eccentric, inclined resonant KBOs
remains a challenge.
