From Classical Mechanics, Gregory, in the chapter on Hamilton's equations of motion:
14.13: Decide if the energy surfaces in phase space are bounded for the following cases:
i.) The two-body gravitation problem with E<0
ii.) The two-body gravitation problem viewed from the zero-momentum frame with E<0
iii.) The three-body gravitation problem viewed from the zero-momentum frame with E<0. Does the Solar System have the recurrence property?
Hamilton's equations, Lioville's theorem, Poincare's recurrence theorem.
The Attempt at a Solution
The trouble here is that the chapter has not explained what an "energy surface in phase space" is or how one is to judge whether or not it's bounded. Can someone please help me understand what that means?