Serge Tabachnikov

activity

20212025

most citedA family of integrable transformations of centroaffine polygons: geometrical aspects

1 citations · 1 across the 4 of their papers we have counts for

collaborators

Showing math.DSShow all

3 papers · 1 filter

math.DS2025

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…

math.DS2024

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…

math.DS2021★ 1 cited

A family of integrable transformations of centroaffine polygons: geometrical aspects

M. Arnold, D. Fuchs, S. Tabachnikov

Two polygons, $(P_{1}, \dots, P_{n})$ and $(Q_{1}, \dots, Q_{n})$ in $R^{2}$ are $c$ -related if $det (P_{i}, P_{i + 1}) = det (Q_{i}, Q_{i + 1})$ and $det (P_{i}, Q_{i}) = c$ for all $i$ . This relat…