Polygonal bicycle paths and the Darboux transformation

Alevy, Ian; Tsukerman, Emmanuel

doi:10.2140/involve.2016.9.57

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Polygonal bicycle paths and the Darboux transformation

Ian Alevy and Emmanuel Tsukerman

Vol. 9 (2016), No. 1, 57–66

DOI: 10.2140/involve.2016.9.57

Abstract

A bicycle $(n, k)$ -gon is an equilateral $n$ -gon whose $k$ diagonals are of equal length. In this paper we introduce periodic bicycle $(n, k)$ -paths, which are a natural variation in which the polygon is replaced with a periodic polygonal path, and study their rigidity and integrals of motion.

Keywords

bicycle polygons, tire track problem, floating bodies in equilibrium

Mathematical Subject Classification 2010

Primary: 37J35, 52C25

Milestones

Received: 7 September 2013

Revised: 1 September 2014

Accepted: 8 December 2014

Published: 17 December 2015

Communicated by Kenneth S. Berenhaut

Authors

Ian Alevy
Division of Applied Mathematics Brown University Providence, RI 02912 United States

Emmanuel Tsukerman
Department of Mathematics University of California, Berkeley Berkeley, CA 94720 United States

Vol. 9, No. 1, 2016