The main purpose is to describe the evolution of $\Xt = \Xs \wedge_- \Xss,$ with $\X(s,0)$ a regular polygonal curve with a nonzero torsion in the 3-dimensional hyperbolic space. Unlike in the Euclidean space, a nonzero torsion implies two different helical curves. However, recent techniques developed by de la Hoz, Kumar, and Vega help us in describing the evolution at rational times both theoretically and numerically, and thus, the similarities and differences. Numerical experiments show that the trajectory of the point $\X(0,t)$ exhibits new variants of Riemann's non-differentiable function whose structure depends on the initial torsion in the problem. As a result, with these new solutions, it is shown that the smooth solutions (helices, straight line) in the hyperbolic space show the same instability as displayed by their Euclidean counterparts and curves with zero-torsion. These numerical observations are in agreement with some recent theoretical results obtained by Banica and Vega.

翻译：主要目的是描述$\Xt =\ X =\ xwedge_ -\ xs, 美元=xx, 美元=X, 美元=0, 普通多边形曲线, 在三维双曲空间内为非零压度。 与欧几里德空间不同, 非零压度意味着两种不同的螺旋曲线。 然而, 由德拉霍兹、 库马尔和维加开发的最新技术帮助我们描述理性时间( 理论和数值)的进化过程, 从而描述相似性和差异。 数字实验显示, 点的轨迹 $\X( 0. t) 显示, Riemann 的无差别功能有新的变体, 其结构取决于问题的初始向量。 结果显示, 有了这些新解决方案, 超偏差空间的平滑解( 安全、 直线) 显示的不稳定性与 Euclidean 对应方和 曲线显示的零振荡一样。 这些数字观测结果与Banica 和 Vega最近获得的一些理论结果是一致的。