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概念，如连贯结构、模式和间歇性。为了做到这一点，他将研究一些类耦合映射格的行为，这些格最纯粹地展示了这些类型的运动。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的系统的第一个例子的热力学极限，来考虑扩展系统中输运的相关问题。这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。在“动力学”的标题下，可以放置关于抽象变换如何作用于光滑空间的现代理论。通过这种方式，遍历理论在寻求对均匀空间上的流进行分类时与几何接触。

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.