New Aspects of non-thermal chaos and ergodic problem

具有多个自由度的保守系统（哈密顿系统）的动力学性质不仅从非线性动力学的观点来看，而且作为统计物理学的基本问题，在诸如化学反应的系统中，组分（分子）的动力学行为是重要的，这是非常有趣和重要的。在动力系统理论中，一个被称为“阿诺德扩散”的过程被认为是具有多个自由度的哈密顿系统的典型行为，并且是松弛的基本过程。关于Arnold扩散，我们澄清了Arnold扩散确实存在，以前用线性扰动分析得到的关于Arnold扩散的大小的估计是正确的，虽然它被称为“扩散”，但Arnold扩散具有很强的时间相关性，与布朗运动驱动的普通扩散相反。这些结果可以说，关于Arnold扩散的知识有了很大的增加。此外，我们 ...更多信息 Arnold扩散具有很强的时间相关性，这意味着在化学反应系统和生物系统中的分子等低自由度系统中，从运动方程而不是从热涨落的角度来重新研究动力学行为是很重要的.对于动力学结构的形成，我们引入了一个新的模型来进一步研究我们在质量片模型中发现的分形结构的机制.模型中的两体相互作用势被推广到幂律型，|R| ^k，其中r是两个粒子之间的距离，“k”是一个正参数。不同的参数k值会导致两体关联的不同行为，并且我们发现，两体势是幂律型的事实并不总是产生幂律型关联。本文是在“第三届21COE会议：2005年9月在早稻田大学举行的“天体物理学作为跨学科科学”研讨会。少

Dynamical properties of conservative systems (Hamiltonian systems) with many degrees of freedom are quite interesting and important, not only from the viewpoint of nonlinear dynamics but also as a fundamental problem of statistical physics, and in systems such as in chemical reaction where dynamical behavior of components (molecules) is important. In dynamical systems theory a process called "Arnold diffusion" is expected as a typical behavior of Hamiltonian systems with many degrees of freedom and as a fundamental process of relaxation. About Arnold diffusion we have clarified-- the Arnold diffusion really exists-- the estimation about the magnitude of Arnold diffusion previously obtained from linear perturbation analysis is correct-- although it is called "diffusion", Arnold diffusion has strong temporal correlation, contrary to ordinary diffusion driven by Brownian motion.With these results it can be said that the knowledge about Arnold diffusion has progessed much.In addition, our … More finding that Arnold diffusion has strong temporal correlation implies that, in chemical reaction systems and molecules in bio systems, few degrees of systems, it is important to reinvestigate the dynamical behavior not from thermal fluctuation but from equation of motion.As for dynamical structure formation, we introduced a new model to investigate further the mechanism of fractal structure we had discovered in mass-sheet model. In the model two-body interaction potential is extended to power-law type of |r|^k, where r is the distance between two particles and "k" is a positive parameter. Different values of the parameter "k" give rise to different behavior in two-body correlation, and we found that the fact that two-body potential is power-law type does not always produce power-law type correlation.A general review talk about dynamical structure formation and Hamiltonian dynamical systems is presented as invited talk in a conference "The Third 21COE symposium : Astrophysics as Interdisciplinary Science" held at Waseda University in Sep.2005. Less