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Results tagged with billiards
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user 2954
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.
22
votes
Can every $\mathbb{Z}^2$ disk be pinball-reached?
Let $C_r(x,y)$ or $C(x,y)$ be the circle of radius $r$ about the lattice point $(x,y)$.
Suppose we choose a sequence of circles to hit, and ask for the piecewise linear path of shortest length from t …
- 151k
29
votes
What "real life" problems can be solved using billiards?
A complication not present in the usual mathematical billiards is that the gain region may have a different index of refraction from the surrounding medium, so light entering it at an angle may be deflected …
- 28k
6
votes
Accepted
Well-definedness of single-particle smooth billiards flow
I think the paper you want is B. Halpern, "Strange Billiard Tables." Transactions of the AMS Vol 232, 1977.
Thanks to Carl for pointing out that Halpern considers tables with the additional condition …
- 28k