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This content will become publicly available on January 1, 2026

Title: 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 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.  more » « less
Award ID(s):
2404535
PAR ID:
10588169
Author(s) / Creator(s):
Publisher / Repository:
THEORETICAL AND APPLIED MECHANICS
Date Published:
Journal Name:
Theoretical and Applied Mechanics
Issue:
00
ISSN:
1450-5584
Page Range / eLocation ID:
4 to 4
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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