[{"oa_version":"Published Version","type":"journal_article","intvolume":"        44","fulldoi":"https://doi.org/10.3934/dcds.2024059","oa":1,"issue":"11","date_created":"2024-07-14T22:01:10Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.3934/dcds.2024059"}],"citation":{"mla":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11, AIMS, 2024, pp. 3287–301, doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>.","ama":"Fiorebe C. Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. 2024;44(11):3287-3301. doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>","chicago":"Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS, 2024. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>.","short":"C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024) 3287–3301.","apa":"Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic orbits. <i>Discrete and Continuous Dynamical Systems- Series A</i>. AIMS. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/10.3934/dcds.2024059</a>","ista":"Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.","ieee":"C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,” <i>Discrete and Continuous Dynamical Systems- Series A</i>, vol. 44, no. 11. AIMS, pp. 3287–3301, 2024."},"publication_status":"published","language":[{"iso":"eng"}],"publisher":"AIMS","page":"3287-3301","abstract":[{"lang":"eng","text":"In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4."}],"year":"2024","corr_author":"1","day":"01","publication_identifier":{"eissn":["1553-5231"],"issn":["1078-0947"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001230091000001"]},"date_updated":"2026-08-12T06:19:26Z","article_processing_charge":"No","title":"Examples of projective billiards with open sets of periodic orbits","author":[{"first_name":"Corentin","last_name":"Fiorebe","full_name":"Fiorebe, Corentin","id":"06619f18-9070-11eb-847d-d1ee780bd88b"}],"ddc":["500"],"isi":1,"OA_type":"free access","scopus_import":"1","_id":"17231","volume":44,"article_type":"original","date_published":"2024-11-01T00:00:00Z","department":[{"_id":"VaKa"}],"doi":"10.3934/dcds.2024059","status":"public","quality_controlled":"1","month":"11","publication":"Discrete and Continuous Dynamical Systems- Series A"},{"status":"public","doi":"10.1007/s40598-022-00198-y","quality_controlled":"1","month":"10","publication":"Arnold Mathematical Journal","article_type":"original","date_published":"2022-10-01T00:00:00Z","department":[{"_id":"VaKa"}],"author":[{"full_name":"Bialy, Misha","first_name":"Misha","last_name":"Bialy"},{"full_name":"Fiorebe, Corentin","id":"06619f18-9070-11eb-847d-d1ee780bd88b","first_name":"Corentin","last_name":"Fiorebe"},{"full_name":"Glutsyuk, Alexey","last_name":"Glutsyuk","first_name":"Alexey"},{"first_name":"Mark","last_name":"Levi","full_name":"Levi, Mark"},{"full_name":"Plakhov, Alexander","first_name":"Alexander","last_name":"Plakhov"},{"full_name":"Tabachnikov, Serge","first_name":"Serge","last_name":"Tabachnikov"}],"conference":{"location":"Hybrid","end_date":"2021-10-08","start_date":"2021-10-04","name":"CIRM: Centre International de Rencontres Mathématiques"},"volume":8,"scopus_import":"1","_id":"10706","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"link":[{"relation":"earlier_version","url":"https://conferences.cirm-math.fr/2383.html"}]},"external_id":{"arxiv":["2110.10750"]},"article_processing_charge":"No","title":"Open problems on billiards and geometric optics","date_updated":"2023-02-27T07:34:08Z","day":"01","year":"2022","publication_identifier":{"issn":["2199-6792"],"eissn":["2199-6806"]},"page":"411-422","publisher":"Springer Nature","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"This is a collection of problems composed by some participants of the workshop “Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM on October 4–8, 2021."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2110.10750"}],"publication_status":"published","citation":{"ieee":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, and S. Tabachnikov, “Open problems on billiards and geometric optics,” <i>Arnold Mathematical Journal</i>, vol. 8. Springer Nature, pp. 411–422, 2022.","apa":"Bialy, M., Fiorebe, C., Glutsyuk, A., Levi, M., Plakhov, A., &#38; Tabachnikov, S. (2022). Open problems on billiards and geometric optics. <i>Arnold Mathematical Journal</i>. Hybrid: Springer Nature. <a href=\"https://doi.org/10.1007/s40598-022-00198-y\">https://doi.org/10.1007/s40598-022-00198-y</a>","ista":"Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. 2022. Open problems on billiards and geometric optics. Arnold Mathematical Journal. 8, 411–422.","chicago":"Bialy, Misha, Corentin Fiorebe, Alexey Glutsyuk, Mark Levi, Alexander Plakhov, and Serge Tabachnikov. “Open Problems on Billiards and Geometric Optics.” <i>Arnold Mathematical Journal</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s40598-022-00198-y\">https://doi.org/10.1007/s40598-022-00198-y</a>.","short":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold Mathematical Journal 8 (2022) 411–422.","mla":"Bialy, Misha, et al. “Open Problems on Billiards and Geometric Optics.” <i>Arnold Mathematical Journal</i>, vol. 8, Springer Nature, 2022, pp. 411–22, doi:<a href=\"https://doi.org/10.1007/s40598-022-00198-y\">10.1007/s40598-022-00198-y</a>.","ama":"Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. Open problems on billiards and geometric optics. <i>Arnold Mathematical Journal</i>. 2022;8:411-422. doi:<a href=\"https://doi.org/10.1007/s40598-022-00198-y\">10.1007/s40598-022-00198-y</a>"},"arxiv":1,"type":"journal_article","oa_version":"Preprint","oa":1,"fulldoi":"https://doi.org/10.1007/s40598-022-00198-y","intvolume":"         8","date_created":"2022-01-30T23:01:34Z"}]