  We apply a generalized Kepler map theory to describe the qualitative chaotic
dynamics around cometary nuclei, based on accessible observational data for
five comets whose nuclei are well-documented to resemble dumb-bells. The sizes
of chaotic zones around the nuclei and the Lyapunov times of the motion inside
these zones are estimated. In the case of Comet 1P/Halley, the circumnuclear
chaotic zone seems to engulf an essential part of the Hill sphere, at least for
orbits of moderate to high eccentricity.
