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 ${\mathbb{R}}^2$ 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…