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arXiv · 2111.10000

Resonance of ellipsoidal billiard trajectories and extremal rational functions

Vladimir Dragovic·Milena Radnovic
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Abstract

We study resonant billiard trajectories within quadrics in the $d$-dimensional Euclidean space. We relate them to the theory of approximation, in particular the extremal rational functions on the systems of $d$ intervals on the real line. This fruitful link enables us to prove fundamental properties of the billiard dynamics and to provide a comprehensive study of a large class of non-periodic trajectories of integrable billiards. A key ingredient is a functional-polynomial relation of a generalized Pell type. Applying further these ideas and techniques to $s$-weak billiard trajectories, we come to a functional-polynomial relation of the same generalized Pell type.

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Vladimir Dragovic, Milena Radnovic. 2021-11-19. Resonance of ellipsoidal billiard trajectories and extremal rational functions. https://arxiv.org/abs/2111.10000

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