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arXiv · 1602.02699

A family of projectively natural polygon iterations

Quang-Nhat Le
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Abstract

The pentagram map was invented by Richard Schwartz in his search for a projective-geometric analogue of the midpoint map. It turns out that the dynamical behavior of the pentagram map is totally different from that of the midpoint map. Recently, Schwartz has constructed a related map, the projective heat map, which empirically exhibits similar dynamics as the midpoint map. In this paper, we will demonstrate that there is a one-parameter family of maps which behaves a lot like Schwartz's projective heat map.

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Quang-Nhat Le. 2016-02-08. A family of projectively natural polygon iterations. https://arxiv.org/abs/1602.02699

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