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Results tagged with billiards
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user 13832
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.
10
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1
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Does the $n$-gonal billiards conjecture follow from the $m$-gonal conjecture when $m>n$?
I.e., does the $3$-gonal billiards conjecture follow from the $m$-gonal billiards conjecture for any $m>3$? … Furthermore, does the $n$-gonal billiards conjecture follow from the $m$-gonal billiards conjecture for any $n$ and $m>n$?
There is one case for which this is easily seen. …
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5
votes
1
answer
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Unfoldings of trajectories on the Veech triangle $V_4$
$V_4$ is a Veech triangle, so the dynamics of billiards on it are very well understood.
Above is the unfolding of $V_4$, with edge identification indicated by numeral. …
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4
votes
0
answers
83
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Do identical orbit tiles imply identical combinatorial types?
Given a periodic trajectory on a triangle, we can associate to this trajectory a sequence of integers $1,2$ and $3$ by labeling the edges of the triangle and taking the sequence of edges the trajector …
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3
votes
0
answers
141
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Reference for standard lemmas in polygonal billiards
I'm trying to track down references for a couple of well-known results in the theory of polygonal billiards for a paper I'm working on. … This is stated for example in Section 2.1 of "Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories" by R. E. …
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1
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1
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Computing saddle connections in flat structures
Background: A polygonal billiards table $P$ with rational angles gives rise to a flat structure $S(P)$ in a standard way, described here. …
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