{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-02-22T15:58:42Z","has_accepted_license":"1","external_id":{"arxiv":["1912.12685"]},"author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2548-617X","last_name":"Akopyan","full_name":"Akopyan, Arseniy"},{"full_name":"Karasev, Roman","first_name":"Roman","last_name":"Karasev"}],"quality_controlled":"1","doi":"10.1007/s40879-020-00405-0","year":"2022","_id":"7791","month":"12","publication":"European Journal of Mathematics","citation":{"ieee":"A. Akopyan and R. Karasev, “When different norms lead to same billiard trajectories?,” <i>European Journal of Mathematics</i>, vol. 8, no. 4. Springer Nature, pp. 1309–1312, 2022.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312.","ama":"Akopyan A, Karasev R. When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. 2022;8(4):1309-1312. doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>","chicago":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>.","apa":"Akopyan, A., &#38; Karasev, R. (2022). When different norms lead to same billiard trajectories? <i>European Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40879-020-00405-0\">https://doi.org/10.1007/s40879-020-00405-0</a>","mla":"Akopyan, Arseniy, and Roman Karasev. “When Different Norms Lead to Same Billiard Trajectories?” <i>European Journal of Mathematics</i>, vol. 8, no. 4, Springer Nature, 2022, pp. 1309–12, doi:<a href=\"https://doi.org/10.1007/s40879-020-00405-0\">10.1007/s40879-020-00405-0</a>.","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312."},"volume":8,"ddc":["510"],"scopus_import":"1","publication_status":"published","license":"https://creativecommons.org/licenses/by/4.0/","acknowledgement":"AA was supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 78818 Alpha). RK was supported by the Federal professorship program Grant 1.456.2016/1.4 and the Russian Foundation for Basic Research Grants 18-01-00036 and 19-01-00169. Open access funding provided by Institute of Science and Technology (IST Austria). The authors thank Alexey Balitskiy, Milena Radnović, and Serge Tabachnikov for useful discussions.","status":"public","article_processing_charge":"Yes (via OA deal)","title":"When different norms lead to same billiard trajectories?","date_created":"2020-05-03T22:00:48Z","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:48:03Z","publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"intvolume":"         8","project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"day":"01","page":"1309 - 1312","issue":"4","article_type":"original","publisher":"Springer Nature","file":[{"creator":"dernst","checksum":"f53e71fd03744075adcd0b8fc1b8423d","date_updated":"2020-07-14T12:48:03Z","file_size":263926,"date_created":"2020-05-04T10:33:42Z","content_type":"application/pdf","relation":"main_file","file_name":"2020_EuropMathematics_Akopyan.pdf","file_id":"7796","access_level":"open_access"}],"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2022-12-01T00:00:00Z","oa_version":"Published Version","oa":1,"ec_funded":1,"abstract":[{"text":"Extending a result of Milena Radnovic and Serge Tabachnikov, we establish conditionsfor two different non-symmetric norms to define the same billiard reflection law.","lang":"eng"}],"department":[{"_id":"HeEd"}]}