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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.
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Accepted
Does the random Lorenz gas have a non-trivial diffusion coefficient?
I don't think such a theorem has been proved for the random Lorentz gas. First I want to point out that Sinai proved those scaling limit results for the case of (2D) periodic Lorentz gas with finite h …
- 2,821
17
votes
A special tessellation
Suppose your polygon has angles $\alpha_i=\frac{\pi}{k_i}$ where $k_i\geq 2$ are integers. Then they must satisfy
$$\frac{1}{k_1}+\frac{1}{k_2}+\cdots+\frac{1}{k_n}=n-2,$$
which means $n-2\leq \frac{ …
- 85.6k