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Finiteness theorems on elliptical billiards and a variant of the Dynamical Mordell-Lang Conjecture
[article]
2021
arXiv
pre-print
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in (0,π), there are only finitely many cases for both trajectories being periodic. Another instance is the finiteness of the billiard shots which send a given ball into another one so that this falls eventually in a hole. These results have their origin in 'relative'
arXiv:2103.11347v2
fatcat:63tc47p5fzf7zia4nt7x6ps6om