Finiteness theorems on elliptical billiards and a variant of the Dynamical Mordell-Lang Conjecture
Pietro Corvaja,
Umberto Zannier
Abstract: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' cases of the Manin… Show more
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