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1992 The pentagram map
Richard Schwartz
Experiment. Math. 1(1): 71-81 (1992).

Abstract

We consider the pentagram map on the space of plane convex pentagons obtained by drawing a pentagon's diagonals, recovering unpublished results of Conway and proving new ones. We generalize this to a "pentagram map'' on convex polygons of more than five sides, showing that iterated images of any initial polygon converge exponentially fast to a point. We conjecture that the asymptotic behavior of this convergence is the same as under a projective transformation. Finally, we show a connection between the pentagram map and a certain flow defined on parametrized curves.

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Richard Schwartz. "The pentagram map." Experiment. Math. 1 (1) 71 - 81, 1992.

Information

Published: 1992
First available in Project Euclid: 26 March 2003

zbMATH: 0765.52004
MathSciNet: MR93H:52002

Subjects:
Primary: 52A10

Rights: Copyright © 1992 A K Peters, Ltd.

JOURNAL ARTICLE
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Vol.1 • No. 1 • 1992
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