On cusps of caustics by reflection in two dimensional projective Finsler metrics
Given a projective Finsler metric in a convex domain in the projective plane, that is, a metric in which geodesics are straight lines, consider the respective Finsler billiard system. Choose a generic point inside the table and consider the billiard trajectories that start at this point and undergo...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2025-01-01
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| Series: | Theoretical and Applied Mechanics |
| Subjects: | |
| Online Access: | https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500004T.pdf |
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| Summary: | Given a projective Finsler metric in a convex domain in the projective plane, that is, a metric in which geodesics are straight lines, consider the respective Finsler billiard system. Choose a generic point inside the table and consider the billiard trajectories that start at this point and undergo N reflection off the boundary. The envelope of the resulting 1-parameter family of straight lines is the Nth caustic by reflection. We prove that, for every N, it has at least four cusps, generalizing a similar result for Euclidean metric, obtained recently jointly with G. Bor. |
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| ISSN: | 1450-5584 2406-0925 |