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2001 The Pentagram Map is Recurrent
Richard Evan Schwartz
Experiment. Math. 10(4): 519-528 (2001).

Abstract

The pentagram map is defined on the space of convex $n$-gons (considered up to projective equivalence) by drawing the diagonals that join second-nearest-neighbors in an $n$-gon and taking the new $n$-gon formed by the intersections. We prove that this map is recurrent; thus, for almost any starting polygon, repeated application of the pentagram map will show a near copy of the starting polygon appear infinitely often under various perspectives.

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Richard Evan Schwartz. "The Pentagram Map is Recurrent." Experiment. Math. 10 (4) 519 - 528, 2001.

Information

Published: 2001
First available in Project Euclid: 26 November 2003

zbMATH: 1013.52003
MathSciNet: MR1881752

Rights: Copyright © 2001 A K Peters, Ltd.

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Vol.10 • No. 4 • 2001
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