Abstract

A two-dimensional diagonal system of ordinary differential equations is constructed. The system possesses the following properties: the solution of the Cauchy problem with computable initial condition is a computable function, the lower Lyapunov exponent is noncomputable, and the upper central exponent of the system does not coincide with the higher Lyapunov exponent and is noncomputable.

中文翻译：

---

常微分方程组指数不可计算性的一个例子

摘要

构造了二维常微分方程对角系统。该系统具有以下性质：初始条件可计算的柯西问题的解是一个可计算的函数，下Lyapunov指数是不可计算的，系统的上中心指数与较高的Lyapunov指数不重合且不可计算。