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In short my question is: what can we say about the quotient topology induced by the linear flow on a two-torus? I know that an irrational slope leads to a dense winding and hence (if I'm not mistaken) ...

I have been trying to simulate the behavior of a light particle being reflected inside of a torus (essentially a 3D billiards problem). I have found that after a few thousand bounces, it converges on "...