Examples of projective billiards with open sets of periodic orbits Fiorebe, Corentin 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. American Institute of Mathematical Sciences 2024 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/17231 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> eng info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2024059 info:eu-repo/semantics/altIdentifier/issn/1078-0947 info:eu-repo/semantics/altIdentifier/e-issn/1553-5231 info:eu-repo/semantics/altIdentifier/wos/001230091000001 info:eu-repo/semantics/openAccess