Robust dynamics, invariant structures and topological classification

Abstract

This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with topology. We also present recent examples which introduce a challenge in the classification program and we propose some steps to continue this classification. Finally, we give some suggestions on what to do after classification is achieved.

19 pages, 2 figures. Invited paper Dynamical Systems session in ICM 2018. http://www.icm2018.org