Pentagram Rigidity for Centrally Symmetric Octagons

Author:

Evan Schwartz Richard1

Affiliation:

1. Department of Mathematics , Brown University, 151 Thayer Street, Providence, RI 02912 , USA

Abstract

Abstract In this paper I will establish a special case of a conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. The special case is that of the $3$-diagonal map acting on affine equivalence classes of centrally symmetric octagons. The proof involves establishing that the map is Arnold-Liouville integrable in this case, and then exploring the Lagrangian surface foliation in detail.

Funder

N.S.F

Publisher

Oxford University Press (OUP)

Reference26 articles.

1. Hexagonal circle patterns and integrable systems: patterns with the multi-ratio property and Lax equations on the regular triangular lattice;Bobenko,2001

2. Octagrammum Miysticum and the Golden cross ratio;Evans;Math. Gaz.,2002

3. The limit point of the pentagram map;Glick;Int. Math. Res. Notices,2020

4. The pentagram map and $\mathrm{Y}$-patterns;Glick;Adv. Math.,2012

5. Higher pentagram maps, weighted directed networks, and cluster dynamics;Gekhtman;Electron. Res. Announc. Math. Sci.,2012

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