Regular simplex and periodic billiard orbit

Details Regular simplex and periodic billiard orbit Regular simplex and periodic billiard orbit

2011-12-11

arxiv.org/abs/1112.2370v1

Mathematics

Dynamical Systems

10 pages, 4 figures

Scientific paper

We consider billiard inside regular simplex of $\mathbb{R}^n$. We show the
existence of two periodic trajectories. One of period $n+1$ which passes one
time by each face and one of period $2n$ which passes $n$ times through one
face and one time through each other face. In both cases we obtain exact
coordinates for the periodic points.

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