The Lyapunov exponent is used to quantify the chaos of a dynamical system, by characterizing the exponential sensitivity of an initial point on the dynamical system. However, we cannot directly compute the Lyapunov exponent for a dynamical system without its dynamical equation, although some estimation methods do exist. Information dynamics introduces the entropic chaos degree to measure the strength of chaos of the dynamical system. The entropic chaos degree can be used to compute the strength of chaos with a practical time series. It may seem like a kind of finite space Kolmogorov-Sinai entropy, which then indicates the relation between the entropic chaos degree and the Lyapunov exponent. In this paper, we attempt to extend the definition of the entropic chaos degree on a d-dimensional Euclidean space to improve the ability to measure the stength of chaos of the dynamical system and show several relations between the extended entropic chaos degree and the Lyapunov exponent.

Lyapunov指数通过表征动力学系统上初始点的指数敏感性来量化动力学系统的混沌。但是，尽管确实存在一些估计方法，但是如果没有动力学方程，我们就无法直接为动力学系统计算Lyapunov指数。信息动力学引入熵混沌度来度量动力学系统的混沌强度。熵混沌度可用于计算具有实际时间序列的混沌强度。它看起来像是一种有限空间的Kolmogorov-Sinai熵，然后表明熵混沌程度与Lyapunov指数之间的关系。在本文中，我们尝试在d上扩展熵混沌度的定义。维欧几里德空间，提高了测量动力学系统混沌强度的能力，并显示了扩展的熵混沌度与Lyapunov指数之间的几种关系。