A Textbook Case of Pentagram Rigidity
Dynamical Systems
2021-11-16 v3
Abstract
In this paper I will explain a rigidity conjecture that intertwines the deep diagonal pentagram maps and Poncelet polygons. I will also establish a simple case of the conjecture, the one involving the -diagonal map on a convex -gon with -fold rotational symmetry. This case involves a textbook analysis of a pencil of elliptic curves.
Keywords
Cite
@article{arxiv.2108.07604,
title = {A Textbook Case of Pentagram Rigidity},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:2108.07604},
year = {2021}
}
Comments
This version is the same as the previous one, except that I remove all the experimental observations about a more general case. I have now proved the more general case and posted it on the arXiv as a companion paper