Chaos and resonances in the Edgeworth-Kuiper-belt

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Selected resonant areas in the Edgeworth-Kuiper-belt will be investigated, especially the 4:7, 3:5 and the 1:2 resonances. Different numerical tools will be employed to study their characteristics, stability and resonance widths. Of special importance will be the implementation of a fairly new chaos indicator (MEGNO) to the problem of asteroid dynamics. With this indicator it will be possible to resolve the fine structure of phase-space such that also resonances of higher order, Kozai resonances etc. become visible. To understand the various signatures found by means of numerical integrations some analytical models will be developed. By means of perturbation theory we will reduce the degrees of freedom of a problem significantly so that it can be solved analytically. This reduction of complexity involves averaging of the Hamiltonian over short periodic perturbations, expansions around an exact resonance point and canonical transformations of variables. The numerical routines will be modified and additional analytical models will be introduced so that also the migration of major planets due to their interactions with planetesimals and its impact onto asteroid dynamics can be investigated.