# Elementary approach to closed billiard trajectories in asymmetric normed spaces

Akopyan A, Balitskiy A, Karasev R, Sharipova A. 2016. Elementary approach to closed billiard trajectories in asymmetric normed spaces. Proceedings of the American Mathematical Society. 144(10), 4501–4513.

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Author

Akopyan, Arseniy

^{ISTA}^{}; Balitskiy, Alexey; Karasev, Roman; Sharipova, AnastasiaDepartment

Abstract

We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results.

Publishing Year

Date Published

2016-10-01

Journal Title

Proceedings of the American Mathematical Society

Acknowledgement

The first and third authors were supported by the Dynasty Foundation. The first, second and third authors were supported by the Russian Foundation for Basic Re- search grant 15-31-20403 (mol a ved).

Volume

144

Issue

10

Page

4501 - 4513

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### Cite this

Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces.

*Proceedings of the American Mathematical Society*. 2016;144(10):4501-4513. doi:10.1090/proc/13062Akopyan, A., Balitskiy, A., Karasev, R., & Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces.

*Proceedings of the American Mathematical Society*. American Mathematical Society. https://doi.org/10.1090/proc/13062Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”

*Proceedings of the American Mathematical Society*. American Mathematical Society, 2016. https://doi.org/10.1090/proc/13062.A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,”

*Proceedings of the American Mathematical Society*, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016.Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.”

*Proceedings of the American Mathematical Society*, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:10.1090/proc/13062.**All files available under the following license(s):**

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