扩展Kolmogorov熵
Extended Kolmogorov Entropy
摘要：
Kolmogorov熵允许将具有等价连续谱的动力系统分裂成非同构子类。在本文中，我们试图概括熵的概念，这将允许分裂系统等效连续谱和相等的Kolmogorov熵成更精细的非同构子类。我们将定义并计算环面上双曲自同构的新度量不变量。环面上的双曲系统是高能物理蒙特卡罗模拟中理想的伪随机数发生器，新的度量不变量使得当它们具有相等的熵时可以更好地描述MC发生器.
英文摘要：
The Kolmogorov entropy allows to split the dynamical systems that have equivalent continuous spectrum into non-isomorphic subclasses. In this paper we make an attempt to generalise the concept of entropy that will allow to split the systems with equivalent continuous spectrum and equal Kolmogorov entropies into finer non-isomorphic subclasses. We will define and calculate the new metrical invariant for the hyperbolic automorphisms on a torus. The hyperbolic systems on a torus are perfect pseudorandom number generators for the Monte-Carlo (MC) simulations in high energy physics, and the new metrical invariant allows a finer characterisation of the MC generators when they have equal entropies.
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