  The 1:N mean motion resonances with Neptune are of particular interest
because they have two asymmetric resonance islands, where the distribution of
trapped objects may bear important clues to the history of the Solar System. To
explore the dynamics of these resonances and to investigate whether the
imprints left by the early stage evolution can be preserved in the resonances,
we conduct a comprehensive analyses on the 1:2 and 1:3 resonances. Adopt mainly
the frequency analysis method, we calculate the proper frequencies of the
motion of objects in the resonances, with which the secular mechanisms that
influence the dynamics are determined. Use the spectral number as an indicator
of orbital regularity, we construct dynamical maps on representative planes. By
comparing the structures in the maps with the locations of the secular
mechanisms, we find that the von-Zeipel-Lidov-Kozai mechanism and the $g=2s$
mechanism destabilize the influenced orbits and portray the overall structure
of the 1:2 and 1:3 resonances. The secular resonance $2g-s=s_8$ opens a channel
for objects to switch between the leading and trailing resonance islands, which
can alter the population ratio between these two islands. The secondary
resonances associated with the quasi 2:1 resonance between Uranus and Neptune
are also detected, and they introduce more chaos to the motion. The fine
dynamical structures of the 1:2 and 1:3 resonances revealed in this paper,
combined with knowledge of resonant capture, provide a compelling explanation
for the eccentricity distribution of observed Twotinos. And we anticipate a
more complete understanding of the history of planetary migration in the Solar
System can be achieved by comparing the results in this paper with the
populations in the 1:N resonances in future when further observations bring us
more objects.
