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Results tagged with billiards
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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.
7
votes
Accepted
Reference question: Poncelet theorem
Poncelet published his theorem ("Poncelet's porism) in 1822, after he returned to France following his captivity as war prisoner in Russia:
J.V. Poncelet, Traité des propriétés projectives des figures …
- 680
27
votes
Accepted
What "real life" problems can be solved using billiards?
The
billiard-ball computer, also known as a conservative logic
circuit, is an idealized model of a reversible mechanical computer
based on Newtonian dynamics, proposed in 1982 by Edward Fredk …
- 188k
28
votes
3D Billiards problem inside a torus
These so-called "whispering gallery modes" are familiar from studies of microcavity lasers; they can trap the light indefinitely, only limited by diffraction; this web site by Jens Nöckel nicely summa …
- 188k
6
votes
Current state of Straus's illumination problem
This started as a comment, but became too long.
It might be worth mentioning that from a physics point of view, this problem has a certain ambiguity that somewhat diminishes its interest: when the wa …
- 188k
4
votes
Existence of nonergodic polygonal billiard
The dynamics of billiard flows in rational polygons (J. Smillie, 2000): The billiard in a rational polygon is ergodic in "almost all" directions, more precisely, the Hausdorff dimension of the set of …
- 188k