A note on the pentagram map and tropical geometry
Tsuyoshi Kato

TL;DR
This paper explores the pentagram map's behavior within tropical geometry, revealing quasi-recursive dynamics and connecting geometric transformations to tropical frameworks.
Contribution
It introduces a novel application of tropical geometry to analyze the pentagram map's action on twisted polygons' moduli space.
Findings
Pentagram map exhibits quasi-recursive behavior in certain domains.
Tropical geometry provides a new framework for understanding the map's dynamics.
Connection established between the pentagram automaton and tropical geometric structures.
Abstract
In this note we study the action of the pentagram map on the moduli space of twisted polygons. The action with respect to the canonical coordinate turns out to be applicable to the framework of tropical geometry. As an application, we induce quasi-recursiveness of the pentagram map on some domain, which is induced from dynamical property of the pentagram automaton.
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Taxonomy
TopicsLogic, programming, and type systems · Polynomial and algebraic computation · Nonlinear Waves and Solitons
