14 citations · 49 across the 18 of their papers we have counts for
19 papers
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…
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…
Dancing polygons, rolling balls and the Cartan-Engel distribution
Gil Bor, Luis Hernández Lamoneda
A pair of planar polygons is "dancing" if one is inscribed in the other and they satisfy a certain cross-ratio relation at each vertex of the circumscribing polygon. Non-degenerate…
Bicycling geodesics are Kirchhoff rods
Gil Bor, Connor Jackman, Serge Tabachnikov
A bicycle path is a pair of trajectories in , the `front' and `back' tracks, traced out by the endpoints of a moving line segment of fixed length (the `bicycle frame…
Chains of path geometries on surfaces: theory and examples
Gil Bor, Travis Willse
We derive the equations of chains for path geometries on surfaces by solving the equivalence problem of a related structure: sub-Riemannian geometry of signature on a conta…
On cusps of caustics by reflection: a billiard variation on Jacobi's Last Geometric Statement
Gil Bor, Serge Tabachnikov
A point source of light is placed inside an oval. The -th caustic by reflection is the envelope of the light rays emanating from the light source after reflections off the c…