Four Cometary Belts Associated with the Orbits of Giant Planets: A New   View of the Outer Solar System's Structure Emerges from Numerical Simulations
  Using numerical simulations, we examine the structure of a cometary population near a massive planet, such as a giant planet of the Solar system, starting with one-planet approximation (the Sun plus one planet). By studying the distributions of comets in semimajor axis, eccentricity, pericenter, and apocenter distances, we have revealed several interesting features in these distributions. The most remarkable ones include (i) spatial accumulation of comets near the planetary orbit (which we call the `cometary belt') and (ii) avoidance of resonant orbits by comets. Then we abandon one-planet approximation and examine as to how a cometary belt is modified when the influence of all four giant planets is taken into consideration. To this end, we simulate a stationary distribution of comets, which results from the gravitational scattering of the Kuiper belt objects on the four giant planets and accounts for the effects of mean motion resonances. Accounting for the influence of four giant planets makes the cometary belts overlapping, but nevertheless keeping almost all their basic features found in one-planet approximation. In particular, the belts maintain the gaps in the (a,e)- and (a,i)-space similar to the Kirkwood gaps in the main asteroid belt. We conclude that the large-scale structure of the Solar system is featured by the four cometary belts expected to contain 20-30 millions of scattered comets, and only a tiny fraction of them is currently visible as Jupiter-, Saturn-, etc. family comets. 
Leonid M. Ozernoy, Nick N. Gorkavyi, Tanya Taidakova