{"publication_identifier":{"eissn":["1553-5231"],"issn":["1078-0947"]},"year":"2024","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"}],"publisher":"American Institute of Mathematical Sciences","issue":"11","article_type":"original","status":"public","department":[{"_id":"VaKa"}],"oa_version":"None","type":"journal_article","citation":{"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>.","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>","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."},"date_created":"2024-07-14T22:01:10Z","scopus_import":"1","article_processing_charge":"No","title":"Examples of projective billiards with open sets of periodic orbits","date_updated":"2024-07-16T07:05:00Z","month":"05","corr_author":"1","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        44","page":"3287-3301","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Discrete and Continuous Dynamical Systems- Series A","day":"01","publication_status":"epub_ahead","date_published":"2024-05-01T00:00:00Z","volume":44,"_id":"17231","doi":"10.3934/dcds.2024059","author":[{"first_name":"Corentin","id":"06619f18-9070-11eb-847d-d1ee780bd88b","last_name":"Fiorebe","full_name":"Fiorebe, Corentin"}]}