Symplectic map description of Halley's comet dynamics

•A two-dimensional symplectic map is build to describe 1P/Halley chaotic dynamics.•The energy transfer (kick function) from Solar system to 1P/Halley is calculated.•Each planet contribution is constituted by a Keplerian and a rotating dipole term.•The Sun movement induces a rotating dipole potential which is non-negligible.•The symplectic Halley map is a reliable description on time scale of 104 years104 years.

We determine the two-dimensional symplectic map describing 1P/Halley chaotic dynamics. We compute the Solar system kick function, i.e. the energy transfer to 1P/Halley along one passage through the Solar system. Each planet contribution to the Solar system kick function appears to be the sum of a Keplerian potential and of a rotating gravitational dipole potential due to the Sun movement around Solar system barycenter. The Halley map gives a reliable description of comet dynamics on time scales of 104 yr104 yr while on a larger scales the parameters of the map are slowly changing due to slow oscillations of orbital momentum.