{"quality_controlled":"1","scopus_import":1,"title":"Elementary approach to closed billiard trajectories in asymmetric normed spaces","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1401.0442"}],"oa_version":"Preprint","issue":"10","publist_id":"5885","language":[{"iso":"eng"}],"intvolume":"       144","day":"01","publisher":"American Mathematical Society","year":"2016","ec_funded":1,"date_published":"2016-10-01T00:00:00Z","_id":"1360","doi":"10.1090/proc/13062","author":[{"id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","first_name":"Arseniy","full_name":"Akopyan, Arseniy"},{"last_name":"Balitskiy","first_name":"Alexey","full_name":"Balitskiy, Alexey"},{"last_name":"Karasev","first_name":"Roman","full_name":"Karasev, Roman"},{"last_name":"Sharipova","first_name":"Anastasia","full_name":"Sharipova, Anastasia"}],"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. "}],"publication_status":"published","publication":"Proceedings of the American Mathematical Society","type":"journal_article","date_updated":"2021-01-12T06:50:09Z","volume":144,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"status":"public","page":"4501 - 4513","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"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","month":"10","date_created":"2018-12-11T11:51:34Z","citation":{"chicago":"Akopyan, Arseniy, Alexey Balitskiy, Roman Karasev, and Anastasia Sharipova. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2016. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>.","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.","apa":"Akopyan, A., Balitskiy, A., Karasev, R., &#38; Sharipova, A. (2016). Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/13062\">https://doi.org/10.1090/proc/13062</a>","mla":"Akopyan, Arseniy, et al. “Elementary Approach to Closed Billiard Trajectories in Asymmetric Normed Spaces.” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10, American Mathematical Society, 2016, pp. 4501–13, doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>.","ama":"Akopyan A, Balitskiy A, Karasev R, Sharipova A. Elementary approach to closed billiard trajectories in asymmetric normed spaces. <i>Proceedings of the American Mathematical Society</i>. 2016;144(10):4501-4513. doi:<a href=\"https://doi.org/10.1090/proc/13062\">10.1090/proc/13062</a>","short":"A. Akopyan, A. Balitskiy, R. Karasev, A. Sharipova, Proceedings of the American Mathematical Society 144 (2016) 4501–4513.","ieee":"A. Akopyan, A. Balitskiy, R. Karasev, and A. Sharipova, “Elementary approach to closed billiard trajectories in asymmetric normed spaces,” <i>Proceedings of the American Mathematical Society</i>, vol. 144, no. 10. American Mathematical Society, pp. 4501–4513, 2016."}}