[{"article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","month":"11","oa_version":"Published Version","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>.","short":"C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024) 3287–3301.","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.","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>","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.","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>."},"author":[{"last_name":"Fiorebe","id":"06619f18-9070-11eb-847d-d1ee780bd88b","full_name":"Fiorebe, Corentin","first_name":"Corentin"}],"type":"journal_article","publication_status":"published","quality_controlled":"1","status":"public","isi":1,"issue":"11","language":[{"iso":"eng"}],"ddc":["500"],"date_updated":"2026-10-21T13:43:42Z","date_created":"2024-07-14T22:01:10Z","department":[{"_id":"VaKa"}],"oa":1,"corr_author":"1","publication_identifier":{"issn":["1078-0947"],"eissn":["1553-5231"]},"_id":"17231","scopus_import":"1","title":"Examples of projective billiards with open sets of periodic orbits","intvolume":"        44","researchdata_availability":"no","date_published":"2024-11-01T00:00:00Z","article_type":"original","year":"2024","doi":"10.3934/dcds.2024059","das_tickbox":"0","fulldoi":"https://doi.org/10.3934/dcds.2024059","day":"01","OA_type":"free access","abstract":[{"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.","lang":"eng"}],"volume":44,"main_file_link":[{"url":"https://doi.org/10.3934/dcds.2024059","open_access":"1"}],"page":"3287-3301","supplementarymaterial":"no","external_id":{"isi":["001230091000001"]},"publication":"Discrete and Continuous Dynamical Systems- Series A","publisher":"AIMS"},{"main_file_link":[{"url":"https://arxiv.org/abs/2110.10750","open_access":"1"}],"page":"411-422","publication":"Arnold Mathematical Journal","external_id":{"arxiv":["2110.10750"]},"publisher":"Springer Nature","arxiv":1,"fulldoi":"https://doi.org/10.1007/s40598-022-00198-y","day":"01","year":"2022","doi":"10.1007/s40598-022-00198-y","volume":8,"abstract":[{"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.","lang":"eng"}],"title":"Open problems on billiards and geometric optics","scopus_import":"1","intvolume":"         8","date_published":"2022-10-01T00:00:00Z","article_type":"original","publication_identifier":{"eissn":["2199-6806"],"issn":["2199-6792"]},"oa":1,"department":[{"_id":"VaKa"}],"_id":"10706","date_created":"2022-01-30T23:01:34Z","date_updated":"2023-02-27T07:34:08Z","status":"public","language":[{"iso":"eng"}],"related_material":{"link":[{"relation":"earlier_version","url":"https://conferences.cirm-math.fr/2383.html"}]},"publication_status":"published","author":[{"last_name":"Bialy","full_name":"Bialy, Misha","first_name":"Misha"},{"full_name":"Fiorebe, Corentin","first_name":"Corentin","last_name":"Fiorebe","id":"06619f18-9070-11eb-847d-d1ee780bd88b"},{"last_name":"Glutsyuk","first_name":"Alexey","full_name":"Glutsyuk, Alexey"},{"last_name":"Levi","first_name":"Mark","full_name":"Levi, Mark"},{"full_name":"Plakhov, Alexander","first_name":"Alexander","last_name":"Plakhov"},{"first_name":"Serge","full_name":"Tabachnikov, Serge","last_name":"Tabachnikov"}],"type":"journal_article","quality_controlled":"1","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"start_date":"2021-10-04","name":"CIRM: Centre International de Rencontres Mathématiques","end_date":"2021-10-08","location":"Hybrid"},"citation":{"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>","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.","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>","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>.","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>.","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.","short":"M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold Mathematical Journal 8 (2022) 411–422."},"oa_version":"Preprint","month":"10"}]