The physical motion of the billiards is two-dimensional, but wouldn’t the phase space be four-dimensional (since it tracks both position and momentum)?
I think the reason chaos needs at least three-dimensional phase space for continuous-time systems is that the orbits in phase space can’t intersect (which the paths of the billiards in real space obviously do).
The physical motion of the billiards is two-dimensional, but wouldn’t the phase space be four-dimensional (since it tracks both position and momentum)?
I think the reason chaos needs at least three-dimensional phase space for continuous-time systems is that the orbits in phase space can’t intersect (which the paths of the billiards in real space obviously do).
You are correct in the identification of the phase space for billiards.