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Results tagged with billiards
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user 94933
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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Current state of Straus's illumination problem
In George W. Tokarsky's Polygonal Rooms Not Illuminable from Every Point (1995) it is stated that the problem
Is a polygonal region illuminable from at least one point in the region?
was still …
- 315
9
votes
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Existence of periodic orbits in rational billiards
Recently I've got interested in dynamical billiards. Some results in this field are obtained by elementary methods. For instance, see George W. … Baxter and Ron Umble's Periodic Orbits of Billiards on an Equilateral Triangle. Then I stumbled across this
Every rational billiard has periodic orbits. …
- 315