Examples of projective billiards with open sets of periodic orbits
Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.
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Abstract
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.
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Date Published
2024-05-01
Journal Title
Discrete and Continuous Dynamical Systems- Series A
Volume
44
Issue
11
Page
3287-3301
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IST-REx-ID
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Fiorebe C. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 2024;44(11):3287-3301. doi:10.3934/dcds.2024059
Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. American Institute of Mathematical Sciences. https://doi.org/10.3934/dcds.2024059
Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” Discrete and Continuous Dynamical Systems- Series A. American Institute of Mathematical Sciences, 2024. https://doi.org/10.3934/dcds.2024059.
C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,” Discrete and Continuous Dynamical Systems- Series A, vol. 44, no. 11. American Institute of Mathematical Sciences, pp. 3287–3301, 2024.
Fiorebe C. 2024. Examples of projective billiards with open sets of periodic orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.
Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic Orbits.” Discrete and Continuous Dynamical Systems- Series A, vol. 44, no. 11, American Institute of Mathematical Sciences, 2024, pp. 3287–301, doi:10.3934/dcds.2024059.
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