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arXiv · 1508.07274

Solitons of discrete curve shortening

Christine Rademacher·Hans-Bert Rademacher
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Abstract

For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called (affine) soliton of the transformation T if its image under T is an affine image of the polygon. We describe a large class of solitons by considering smooth curves which are solutions of a linear system of differential equations of second order with constant coefficients. As examples we obtain solitons lying on spiral curves which under the transformation T rotate and shrink.

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Christine Rademacher, Hans-Bert Rademacher. 2016-06-20. Solitons of discrete curve shortening. https://arxiv.org/abs/1508.07274

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