The Large Scale Structures in the Solar System: I. Cometary Belts With   Resonant Features Near the Orbits of Four Giant Planets
  We employ an efficient numerical approach to simulate a stationary distribution of test objects, which results from their gravitational scattering on the four giant planets, with accounting for effects of mean motion resonances. Using the observed distribution of the Kuiper belt objects, we reconstruct, in the space of orbital coordinates, the distribution function $n(a,e,i)$ for the population of minor bodies beyond Jupiter. We confirm that thousands of large yet cold comets and Centaurs might be located between the orbits of Jupiter and Neptune. Moreover, we find as an important result that they are concentrated into four circumsolar belts, with a highly non-uniform and well structured distribution of the objects. This huge yet unrevealed population, with only a few of its representatives presently known, is expected to have, like our simulations demonstrate, a rich resonant structure containing both density maxima and gaps. The resonant structure is formed due to gravitational perturbations, i.e. in a non-dissipative way. If plotted in the ($a,e,i$)-space of orbital coordinates, the belts contain gaps (including those between resonant groups), quite similar to the Kirkwood gaps in the main asteroid belt. An appreciable fraction of the test bodies reveals, for some time, an accumulation near (rather than in) the resonances, both interior and exterior, with the giant planets. An accompanying paper considers the population simulated in this work as the major source of dust in the outer Solar system. The simple but fast and efficient numerical approach employed in this work would allow the reader for applying it to many other problems of his/her interest. 
Leonid M. Ozernoy, Nikolai N. Gor'kavyi, Tatiana Taidakova