TL;DR
This paper introduces a new geometric construction related to the pentagram map, exploring its basic properties and speculating on its deeper algebraic and integrable structure.
Contribution
It presents a novel geometric construction analogous to logarithmic spirals and investigates its fundamental properties and potential integrability.
Findings
Established basic geometric facts about the construction
Speculated on the algebraic structure and integrability
Connected the construction to the pentagram map
Abstract
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on some of the deeper algebraic structure, such as the complete integrability of the associated dynamical system.
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Taxonomy
TopicsMathematics and Applications · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows