论文标题
Anosov-Kolmogorov的最大混乱动力学系统
Maximally chaotic dynamical systems of Anosov-Kolmogorov
论文作者
论文摘要
最大混乱的K-Systems是具有非零kolmogorov熵的动力系统。另一方面，满足Anosov c条件的双曲动力系统具有相轨迹的指数不稳定性，所有订单的混合，可计数的Lebesgue Spectrum和正kolmogorov熵。 C条件定义了一类丰富的最大混乱系统，这些系统跨越了所有动态系统的空间。对Anosov-Kolmogorov C-K系统的兴趣与试图了解放松现象，统计力学的基础，流体动力学中的湍流的形式，阳米尔斯领域的非线性动力学以及引力n-Body N-Body Systems和Black Hole热动力学的动力学特性有关。在这方面，特殊利益的是C-K系统，这些系统是在负截面曲率和高维托里的Reimannian歧管上定义的。在这里，我们将回顾最大混乱的动力学系统的经典和量子力学特性，即C-K理论在研究Yang-Mills动力学和引力系统的研究中的应用，以及它们在Monte Carlo方法中的应用。
The maximally chaotic K-systems are dynamical systems which have nonzero Kolmogorov entropy. On the other hand, the hyperbolic dynamical systems that fulfil the Anosov C-condition have exponential instability of phase trajectories, mixing of all orders, countable Lebesgue spectrum and positive Kolmogorov entropy. The C-condition defines a rich class of maximally chaotic systems which span an open set in the space of all dynamical systems. The interest in Anosov-Kolmogorov C-K systems is associated with the attempts to understand the relaxation phenomena, the foundation of the statistical mechanics, the appearance of turbulence in fluid dynamics, the non-linear dynamics of the Yang-Mills field as well as the dynamical properties of gravitating N-body systems and the Black hole thermodynamics. In this respect of special interest are C-K systems that are defined on Reimannian manifolds of negative sectional curvature and on a high-dimensional tori. Here we shall review the classical- and quantum-mechanical properties of maximally chaotic dynamical systems, the application of the C-K theory to the investigation of the Yang-Mills dynamics and gravitational systems as well as their application in the Monte Carlo method.
