  Statistical analysis of the orbits of distant Kuiper Belt Objects (KBOs) have
led to suggest that an additional planet should reside in the Solar System.
According to recent models, the secular action of this body should cause
orbital alignment of the KBOs. It was recently claimed that the KBOs concerned
by this dynamics are presumably trapped in mean motion resonances with the
suspected planet. I reinvestigate here the secular model underlying this idea.
The original analysis was done expanding and truncating the secular
Hamiltonian. I show that this is inappropriate here, as the series expansion is
not convergent. I present a study based on numerical computation of the
Hamiltonian with no expansion. I show in phase-space diagrams the existence of
apsidally anti-aligned, high eccentricity libration islands that were not
present in the original modelling, but that match numerical simulations. These
island were claimed to correspond to bodies trapped in mean-motion resonances
with the hypothetical planet, and match the characteristics of the distant KBOs
observed. My main result is that regular secular dynamics can account for the
anti-aligned particles itself as well as mean-motion resonances. I also perform
a semi-analytical study of resonant motion and show that some resonance are
actually capable of producing the same libration islands. I discuss then the
relative importance of both mechanisms.
