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- W4226021322 abstract "Two polygons, $(P_1,ldots,P_n)$ and $(Q_1,ldots,Q_n)$ 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 relation extends to twisted polygons (polygons with monodromy), and it descends to the moduli space of $SL(2,{mathbb R}^2)$-equivalent polygons. This relation is an equiaffine analog of the discrete bicycle correspondence studied by a number of authors. We study the geometry of this relations, present its integrals, and show that, in an appropriate sense, these relations, considered for different values of the constants $c$, commute. We relate this topic with the dressing chain of Veselov and Shabat. The case of small-gons is investigated in detail." @default.
- W4226021322 created "2022-05-05" @default.
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- W4226021322 date "2021-12-15" @default.
- W4226021322 modified "2023-09-24" @default.
- W4226021322 title "A family of integrable transformations of centroaffine polygons: geometrical aspects" @default.
- W4226021322 doi "https://doi.org/10.48550/arxiv.2112.08124" @default.
- W4226021322 hasPublicationYear "2021" @default.
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