Abstract
The methods for an investigation of the evolution of orbits with large eccentricities are presented. The role of resonances in the motion of comets is considered. The expansion of the disturbing function in the restricted three-body problem is obtained for cometary orbits. The method is based on the proximity of cometary eccentricities to 1. The Hamiltonian describing the basic perturbations in the motion of long-period comets is constructed. It leads to mappings for the description of cometary dynamics.
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