Mathematical Sciences: Space-Time and Transport Phenomena inExtended Systems

布尼莫维奇将研究时空混沌的机制，并阐明一些方便和广泛使用但模糊的相干结构、模式和间歇性的概念。为了做到这一点，他将研究一些类别的耦合映射格子的行为，这些格子展示了最纯粹的这些类型的运动。他还将通过研究最近被证明是遍历的任意数量相互作用粒子系统的第一个例子的热力学极限，来考虑扩展系统中的相关输运问题。这个项目涉及对遍历理论的研究。一般说来，遍历理论涉及理解系统的平均行为，这些系统的动力学太复杂或太混乱，以至于无法在微观细节上进行跟踪。在“动力学”的标题下，可以把一组抽象变换如何作用于光滑空间的现代理论放在下面。通过这种方式，遍历理论与几何联系起来，寻求对均匀空间上的流进行分类。

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.