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.
Publishing Year
Date Published
2024-11-01
Journal Title
Discrete and Continuous Dynamical Systems- Series A
Publisher
AIMS
Volume
44
Issue
11
Page
3287-3301
ISSN
eISSN
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. AIMS. 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. AIMS, 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. AIMS, 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, AIMS, 2024, pp. 3287–301, doi:10.3934/dcds.2024059.
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