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The most distant known trans-Neptunian objects (perihelion distance above 38au and semimajor axis above 150 au) are of interest for their potential toreveal past, external, or present but unseen perturbers. Realizing thispotential requires understanding how the known planets influence their orbitaldynamics. We use a recently-developed Poincare mapping approach for orbitalphase space studies of the circular planar restricted three body problem, whichwe have extended to the case of the three-dimensional restricted problem with$N$ planetary perturbers. With this approach, we explore the dynamicallandscape of the 23 most distant TNOs under the perturbations of the knowngiant planets. We find that, counter to common expectations, almost none ofthese TNOs are far removed from Neptune's resonances. Nearly half (11) of theseTNOs have orbits consistent with stable libration in Neptune's resonances; inparticular, the orbits of TNOs 148209 and 474640 overlap with Neptune's 20:1and 36:1 resonances, respectively. Five objects can be ruled currentlynon-resonant, despite their large orbital uncertainties, because our mappingapproach determines the resonance boundaries in angular phase space in additionto semimajor axis. Only three objects are in orbital regions not appreciablyaffected by resonances: Sedna, 2012 VP113 and 2015 KG163. Our analysis alsodemonstrates that Neptune's resonances impart a modest (few percent)non-uniformity in the longitude of perihelion distribution of the currentlyobservable distant TNOs. While not large enough to explain the observedclustering, this small dynamical sculpting of the perihelion longitudes couldbecome relevant for future, larger TNO datasets.

Orbital dynamics landscape near the most distant known trans-Neptunian objects