Dynamics of Partially Hyperbolic Systems

Burns建议研究部分双曲动力系统。他将专注于时间一地图的框架流，紧群扩展的双曲基本集，并延长了普格-舒布定理。该研究将有助于理解部分双曲性，这是混沌系统研究中的基本范式之一，即均匀双曲性的深远扩展。研究结果将在科学文献和讲座中广泛传播。 这项工作也将有助于数学形成的研究生在西北部，部分由PI讲座，部分由学生在他的指导下从事这一工作和相关科目。

Burns proposes to study partially hyperbolic dynamical systems. He will focus on the time-one map of the frame flow, on compact group extensions of hyperbolic basic sets, and on extensions of the Pugh-Shub theorems. The proposed research will contribute to the understanding of partial hyperbolicity, a far-reaching extension of one of the basic paradigms in the study of chaotic systems, namely, uniform hyperbolicity. The results of the research will be broadly disseminated in the scientific literature and in lectures. This work will also contribute to the mathematical formation of graduate students at Northwestern, in part by lectures of the PI, and in part by students working on this and related subjects under his guidance.