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In general, small bodies of the solar system, e.g., asteroids and comets,have a very irregular shape. This feature affects significantly thegravitational potential around these irregular bodies, which hinders dynamicalstudies. The Poincar\'e surface of sec- tion technique is often used to lookfor stable and chaotic regions in two-dimensional dynamic cases. In this work,we show that this tool can be useful for exploring the surroundings ofirregular bodies such as the asteroid 4179 Toutatis. Considering a rotatingsystem with a particle, under the effect of the gravitational field computedthree-dimensionally, we define a plane in the phase space to build thePoincar\'e surface of sections. Despite the extra dimension, the sectionscreated 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 findcorrelations between those regions and the contri- bution of the thirddimension of the system to the trajectory dynamics as well. As examples, weshow details of periodic(resonant or not) and quasi-periodic trajectories.

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