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20212025
most citedA family of integrable transformations of centroaffine polygons: geometrical aspects

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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…

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…