Based on the work of Rodriguez-Hertz, Rodriguez-Hertz, and Ures, it is now known that a partially hyperbolic system may possess a compact embedded submanifold tangent to the center-stable or center-unstable bundle. In this talk, I will describe new examples of these objects both in dimension 3 and in higher dimensions. I will further show that any system can have at most finitely many compact cs-submanifolds and present classification results for 3-dimensional systems with cs-tori.
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