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On general rotation sets of open billiards

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Abstract

We study the general rotation sets of open billiards in \({\mathbb {R}}^2\) for the observable given by the starting point of a given billiard trajectory. We prove that, for a class of open billiards, the general rotation set is equal to the polygon formed by the midpoints of the segments connecting the centers of the obstacles. Moreover, we provide an example to show that such a result may not hold in general.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Western Australia, Perth, WA, 6009, Australia

    Zainab Alsheekhhussain

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  1. Zainab Alsheekhhussain
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Correspondence to Zainab Alsheekhhussain.

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Financial support by the Ministry of Higher Education in Saudi Arabia is gratefully acknowledged.

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Alsheekhhussain, Z. On general rotation sets of open billiards. Arch. Math. 110, 71–80 (2018). https://doi.org/10.1007/s00013-017-1111-7

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  • DOI: https://doi.org/10.1007/s00013-017-1111-7

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