I was e-mailed about reversible systems because of question (1) in homework sheet 1, and here is my answer (that I am posting here because it is relevant for everybody):
I checked the definition of reversible system after the lecture to check
whether I had a typo (given the question that came up). I don't remember
what I wrote on the board, but the one in the scanned lecture notes is
correct. Because of that, I didn't bring it up again in lecture the next
In fact, it should be g(x,-y) = g(x,y), so it sounds like I put an extra
minus sign in the lectures.
You want invariance under (t,y) -> (-t,-y).