2 papers
math.DG2025
Bicycle tracks with hyperbolic monodromy -- results and conjectures
G. Bor, L. Hernández-Lamoneda, S. Tabachnikov
We find new necessary and sufficient conditions for the bicycling monodromy of a closed plane curve to be hyperbolic. Our main tool is the ``hyperbolic development" interpretation…
math.DG2024
Cusps of caustics by reflection in ellipses
Gil Bor, Mark Spivakovsky, Serge Tabachnikov
This paper is concerned with the billiard version of Jacobi's last geometric statement and its generalizations. Given a non-focal point inside an elliptic billiard table, one c…