Mathematical Sciences: Space-Time and Transport Phenomena inExtended Systems

布尼莫维奇将研究时空混沌的机制， 阐明一些方便的、广泛使用的但模糊的概念， 相干结构、模式和不相干性。 迟浩 我将研究一些耦合映象格子的行为 展示了最纯粹的这种运动。 他将 还考虑到与运输有关的问题， 系统通过调查热力学极限的第一 任意数量相互作用粒子的系统的例子 最近被证明是遍历的 该项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 系统的动力学过于复杂或混乱， 在微观细节上进行跟踪。 在“动态”标题下， 可以把现代理论放在抽象的 变换作用于光滑空间。这样，遍历理论 与几何学接触，以寻求对 齐性空间

Bunimovich will study mechanisms of space-time chaos and elucidate some convenient and widely used but vague notions of coherent structures, patterns and intermittency. To do this, he will study the behavior of some classes of coupled map lattices that demonstrate most purely these types of motion. He will consider also the related problem of transport in extended systems by investigating the thermodynamic limit of the first examples of systems of arbitrary number of interacting particles recently proven to be ergodic. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way, ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.