{"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","date_updated":"2024-02-22T15:58:42Z","month":"12","title":"When different norms lead to same billiard trajectories?","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.","citation":{"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>","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>.","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>.","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.","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>","ista":"Akopyan A, Karasev R. 2022. When different norms lead to same billiard trajectories? European Journal of Mathematics. 8(4), 1309–1312.","short":"A. Akopyan, R. Karasev, European Journal of Mathematics 8 (2022) 1309–1312."},"type":"journal_article","date_created":"2020-05-03T22:00:48Z","has_accepted_license":"1","article_type":"original","status":"public","ec_funded":1,"oa_version":"Published Version","department":[{"_id":"HeEd"}],"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"}],"year":"2022","ddc":["510"],"publication_identifier":{"issn":["2199-675X"],"eissn":["2199-6768"]},"issue":"4","publisher":"Springer Nature","external_id":{"arxiv":["1912.12685"]},"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"author":[{"orcid":"0000-0002-2548-617X","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","full_name":"Akopyan, Arseniy","last_name":"Akopyan","first_name":"Arseniy"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"doi":"10.1007/s40879-020-00405-0","_id":"7791","volume":8,"date_published":"2022-12-01T00:00:00Z","day":"01","publication_status":"published","publication":"European Journal of Mathematics","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","page":"1309 - 1312","file_date_updated":"2020-07-14T12:48:03Z","file":[{"file_size":263926,"date_updated":"2020-07-14T12:48:03Z","creator":"dernst","content_type":"application/pdf","date_created":"2020-05-04T10:33:42Z","file_id":"7796","checksum":"f53e71fd03744075adcd0b8fc1b8423d","file_name":"2020_EuropMathematics_Akopyan.pdf","relation":"main_file","access_level":"open_access"}],"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"intvolume":"         8","language":[{"iso":"eng"}],"quality_controlled":"1"}