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Billiards are a class of dynamical systems in which a point particle moves uniformly in a domain $D\subset \mathbb{R}^d$ except for mirror-like reflections from the boundary. Varying $D$ leads to examples satisfying many ergodic properties. Billiards enhance visual explanations of dynamical concepts to students and the general public. There are many applications in physics and image processing. The free motion and/or reflection rule may be generalized.
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Light rays bouncing in twisted tubes
To spell out the above in more details we can reduce the question to a question of billiards. …
5
votes
Light rays bouncing in twisted tubes
I would like to add one more piece of information and some pictures concerning the snake like tube. All this was communicated to me by Peter Panov.
To analyze the movement of a ray in the tube we wil …