---
_id: '1360'
abstract:
- lang: eng
text: '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. '
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).
article_processing_charge: No
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Alexey
full_name: Balitskiy, Alexey
last_name: Balitskiy
- first_name: Roman
full_name: Karasev, Roman
last_name: Karasev
- first_name: Anastasia
full_name: Sharipova, Anastasia
last_name: Sharipova
citation:
ama: 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/13062
apa: 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. American Mathematical Society. https://doi.org/10.1090/proc/13062
chicago: Akopyan, 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.
ieee: 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.
ista: 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.
mla: 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.
short: A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American
Mathematical Society 144 (2016) 4501–4513.
date_created: 2018-12-11T11:51:34Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2021-01-12T06:50:09Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/proc/13062
ec_funded: 1
intvolume: ' 144'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1401.0442
month: '10'
oa: 1
oa_version: Preprint
page: 4501 - 4513
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Proceedings of the American Mathematical Society
publication_status: published
publisher: American Mathematical Society
publist_id: '5885'
quality_controlled: '1'
scopus_import: 1
status: public
title: Elementary approach to closed billiard trajectories in asymmetric normed spaces
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 144
year: '2016'
...