  In the framework of the planar restricted three body problem we study a
considerable number of resonances associated to the Kuiper Belt dynamics and
located between 30 and 48 a.u. Our study is based on the computation of
resonant periodic orbits and their stability. Stable periodic orbits are
surrounded by regular librations in phase space and in such domains the capture
of trans-Neptunian object is possible. All the periodic orbits found are
symmetric and there is evidence for the existence of asymmetric ones only in
few cases. In the present work first, second and third order resonances are
under consideration. In the planar circular case we found that most of the
periodic orbits are stable. The families of periodic orbits are temporarily
interrupted by collisions but they continue up to relatively large values of
the Jacobi constant and highly eccentric regular motion exists for all cases.
In the elliptic problem and for a particular eccentricity value of the primary
bodies the periodic orbits are isolated. The corresponding families, where they
belong to, bifurcate from specific periodic orbits of the circular problem and
seem to continue up to the rectilinear problem. Both stable and unstable orbits
are obtained for each case. In the elliptic problem the unstable orbits found
are associated with narrow chaotic domains in phase space. The evolution of the
orbits, which are located in such chaotic domains, seems to be practically
regular and bounded for long time intervals.
