Motivated by this question and first line of this answer, I want to ask if we were describe the evolution of an orientable continuous simply connected physical body having mass distribution based on the ideas of Dynamical systems under the gravitational law, what configurations would look like the attractors and repellors? How could the answer change if we increased the genus of the surface?
To clear ambiguity, I am assuming the interior of surface being filled uniformly with some constant mass per volume density $\rho(x)=m$
