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).
I’m not sure what the author had in mind exactly, but it’s not accurate that at least 3D is required in continuous-time systems.
A common example in 2D is the chaotic billiard.
I am not familiar with the book and haven’t studied strange attractors.
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).