1 citations · 1 across the 4 of their papers we have counts for
5 papers
Outer length billiards on a large scale
Peter Albers, Lael Edwards-Costa, Serge Tabachnikov
We present some foundational results about the outer length billiard system, including its generating function and the invariant area form. We describe the limiting behavior of the…
On cusps of caustics by reflection in two dimensional projective Finsler metrics
Serge Tabachnikov
A Finsler, not necessarily symmetric, metric in the plane or its convex subset is called projective if its geodesics are straight segments. We consider Finsler billiards in a conve…
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…
A family of maps and a vector field on plane polygons
Maxim Arnold, Lael Costa, Serge Tabachnikov
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discre…
A family of integrable transformations of centroaffine polygons: geometrical aspects
M. Arnold, D. Fuchs, S. Tabachnikov
Two polygons, and in are -related if and for all . This relat…