article Examples of projective billiards with open sets of periodic orbits published yes Corentin Fiorebe author 06619f18-9070-11eb-847d-d1ee780bd88b VaKa department 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 Sciences2024 eng Discrete and Continuous Dynamical Systems- Series A 1078-0947 1553-5231 00123009100000110.3934/dcds.2024059 44113287-3301 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> Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301. C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024) 3287–3301. 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> 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>. 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>. 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. 172312024-07-14T22:01:10Z2025-10-16T11:53:22Z