Higher pentagram maps, weighted directed networks, and cluster dynamics

Michael Gekhtman; Michael Shapiro; Serge Tabachnikov; Alek Vainshtein

doi:10.3934/era.2012.19.1

Higher pentagram maps, weighted directed networks, and cluster dynamics

Michael Gekhtman, Michael Shapiro, Serge Tabachnikov, Alek Vainshtein

Research output: Contribution to journal › Article › peer-review

Abstract

The pentagram map was extensively studied in a series of papers by V. Ovsienko, R. Schwartz and S. Tabachnikov. It was recently interpreted by M. Glick as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson geometry of directed networks on surfaces, we generalize Glick's construction to include the pentagram map into a family of geometrically meaningful discrete integrable maps.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Electronic Research Announcements in Mathematical Sciences
Volume	19
DOIs	https://doi.org/10.3934/era.2012.19.1
State	Published - 2012

Keywords

Cluster dynamics
Discrete integrable system
Pentagram map

ASJC Scopus subject areas

General Mathematics

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10.3934/era.2012.19.1

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abstract = "The pentagram map was extensively studied in a series of papers by V. Ovsienko, R. Schwartz and S. Tabachnikov. It was recently interpreted by M. Glick as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson geometry of directed networks on surfaces, we generalize Glick's construction to include the pentagram map into a family of geometrically meaningful discrete integrable maps.",

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AU - Tabachnikov, Serge

AU - Vainshtein, Alek

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AB - The pentagram map was extensively studied in a series of papers by V. Ovsienko, R. Schwartz and S. Tabachnikov. It was recently interpreted by M. Glick as a sequence of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson geometry of directed networks on surfaces, we generalize Glick's construction to include the pentagram map into a family of geometrically meaningful discrete integrable maps.

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KW - Discrete integrable system

KW - Pentagram map

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Higher pentagram maps, weighted directed networks, and cluster dynamics

Abstract

Keywords

ASJC Scopus subject areas

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