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