Does anyone know of an accessible reference that sketches a proof of Poincare's recurrence theorem? (This is not a homework question.) I'm coming up short in my searches -- either the proof is too sketchy, or it is inaccessible to me (little background in maths, but enough to talk about phase points, their trajectories). If possible, I'd like the proof to provide a reductio of the following assumptions: 1. A is a set of phase points in some region of Gamma-space, such that each point in A represents a system with fixed and finite energy E and finite spatial extension. 2. B is a non-empty subset of A consisting of those points on trajectories that never return to A having once left A. 3. The Lebesgue measure of B is both finite and non-zero. I know these three assumptions are jointly inconsistent -- but I can't figure out why. Thanks!