nets takes place. This is because we know from experience that an orbital crossing is very likely to lead to a close encounter in planetary and protoplanetary systems (Yoshinaga， Kokubo & Makino 1999). Of course this statement cannot be simply applied to systems with stable orbital resonances such as the Neptune–Pluto system.
1.2Previous studies and aims of this research
In addition to the vagueness of the concept of stability， the planets in our Solar system show a character typical of dynamical chaos (Sussman & Wisdom 1988， 1992). The cause of this chaotic behaviour is now partly understood as being a result of resonance overlapping (Murray & Holman 1999; Lecar， Franklin & Holman 2001). However， it would require integrating over an ensemble of planetary systems including all nine planets for a period covering several 10 Gyr to thoroughly understand the long-term evolution of planetary orbits， since chaotic dynamical systems are characteri
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