[{"page":"3287-3301","day":"01","volume":44,"type":"journal_article","article_processing_charge":"No","OA_type":"free access","publisher":"American Institute of Mathematical Sciences","publication":"Discrete and Continuous Dynamical Systems- Series A","issue":"11","main_file_link":[{"url":"https://doi.org/10.3934/dcds.2024059","open_access":"1"}],"status":"public","_id":"17231","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"}],"intvolume":"        44","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Examples of projective billiards with open sets of periodic orbits","citation":{"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>","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>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2024059\">https://doi.org/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>. American Institute of Mathematical Sciences, 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.","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. American Institute of Mathematical Sciences, pp. 3287–3301, 2024.","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, American Institute of Mathematical Sciences, 2024, pp. 3287–301, doi:<a href=\"https://doi.org/10.3934/dcds.2024059\">10.3934/dcds.2024059</a>."},"oa":1,"article_type":"original","quality_controlled":"1","corr_author":"1","year":"2024","date_created":"2024-07-14T22:01:10Z","oa_version":"Published Version","scopus_import":"1","month":"11","external_id":{"isi":["001230091000001"]},"language":[{"iso":"eng"}],"date_updated":"2025-10-16T11:53:22Z","author":[{"last_name":"Fiorebe","id":"06619f18-9070-11eb-847d-d1ee780bd88b","full_name":"Fiorebe, Corentin","first_name":"Corentin"}],"date_published":"2024-11-01T00:00:00Z","isi":1,"department":[{"_id":"VaKa"}],"publication_identifier":{"issn":["1078-0947"],"eissn":["1553-5231"]},"doi":"10.3934/dcds.2024059"}]