Dynamics of Partially Hyperbolic Systems

Northwestern University, Evanston IL

Investigators

Abstract

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.