On the Schrödinger map for regular helical polygons in the hyperbolic space

Abstract The main purpose of this article is to understand the evolution X t = s ∧ − ss , with ( 0) a regular polygonal curve nonzero torsion in three-dimensional Minkowski space. Unlike case Euclidean space, now implies two different helical curves. This generalizes recent works by author de la Hoz and Vega on polygons space as well planar Numerical experiments show that trajectory point (0, ) exhibits new variants Riemann’s non-differentiable function whose structure depends initial problem. As result, we observe smooth solutions (helices, straight line) same instability displayed their counterparts curves zero-torsion. These numerical observations are agreement some theoretical results obtained Banica Vega.