Mathematical Sciences: Ergodic Theory and Applications in Combinatorial Number Theory

博舍尼赞将继续他的工作在遍历理论和 组合数论 他将研究同质的 动力系统可能满足的遍历性质，伪 Anosof区间交换映射，α旋转 有界偏导数和符号流 替代品 这项研究将导致对以下方面的定量估计： 上面提到的动力系统的轨道有多好 均匀分布。 这个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

Boshernitzan will continue his work in ergodic theory and combinatorial number theory. He will study the homogenous ergodicity property that dynamical systems may satisfy, pseudo- Anosof interval exchange maps, alpha-rotations with alpha having bounded partial quotients, and symbolic flows coming from substitutions. The study will lead to quantitative estimates on how well the orbits of the above mentioned dynamical systems are uniformly distributed. 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.