Dynamical Resistance Day

Title: Aubry-Mather sets for area-preserving homeomorphisms of the closed annulus (video)

We will review some aspects of the rotation theory for homeomorphisms of the closed annulus preserving boundary components and orientation, relating it to the classical results on rotational behaviour for circle homeomorphisms and for conservative twist maps of the annulus. We will describe the different ways rotational behaviour can be realized, introducing the different rotation sets and rotation vectors that can be associated with these maps. Using some recent techniques recently developed with P. Le Calvez, we will show that for any area-preserving homeomorphism then every rotation vector in the rotation set is realized by a compact invariant set, showing that an analog of the classical Aubry-Mather sets for twist diffeomorphisms exists in this general context. Joint work with Jonathan Conejeros