Discrete monodromy, pentagrams, and the method of condensation
Discrete monodromy, pentagrams, and the method of condensation
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离散单峰、五角星和凝聚法
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
R. Schwartz
中科院分区：
文献类型：
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作者：
R. Schwartz
摘要：本文研究了五芒星映射，它是多边形空间上的一种自然的投影迭代。受常微分方程理论方法的启发，当映射定义在n维空间上时，本文构造了映射的大致n个代数独立的不变量。这些不变量强有力地表明，五角星形映射是一个离散的完全可积系统。该文件还涉及到五角星形地图道奇森的凝聚计算行列式的方法，也被称为八面体递归。
Abstract.This paper studies the pentagram map, a projectively natural iteration on the space of polygons. Inspired by a method from the theory of ordinary differential equations, the paper constructs roughly n algebraically independent invariants for the map, when it is defined on the space of n-gons. These invariants strongly suggest that the pentagram map is a discrete completely integrable system. The paper also relates the pentagram map to Dodgson’s method of condensation for computing determinants, also known as the octahedral recurrence.