Poincar\'e surfaces of section around a 3-D irregular body: The case of asteroid 4179 Toutatis

In general, small bodies of the solar system, e.g., asteroids and comets, have a very irregular shape. This feature affects significantly the gravitational potential around these irregular bodies, which hinders dynamical studies. The Poincar\'e surface of sec- tion technique is often used to look for stable and chaotic regions in two-dimensional dynamic cases. In this work, we show that this tool can be useful for exploring the surroundings of irregular bodies such as the asteroid 4179 Toutatis. Considering a rotating system with a particle, under the effect of the gravitational field computed three-dimensionally, we define a plane in the phase space to build the Poincar\'e surface of sections. Despite the extra dimension, the sections created allow us to find trajec- tories and classify their stabilities. Thus, we have also been able to map stable and chaotic regions, as well as to find correlations between those regions and the contri- bution of the third dimension of the system to the trajectory dynamics as well. As examples, we show details of periodic(resonant or not) and quasi-periodic trajectories.