Raluca Tanase, Institute of Mathematics of the Romanian Academy
We discuss the dynamics of the complex Hénon map, a prototype of a two-dimensional dynamical system exhibiting stretching, folding, chaos and various other coexisting phenomena. We introduce several invariant objects and their dynamical properties, emphasizing important advances in the field. In particular we talk about our recent joint work with T. Firsova on the critical locus, an exotic set associated with the Hénon map. As a diffeomorphism, the Hénon map does not have critical points in the usual sense, but it has a non-empty critical locus (i.e. the set of tangencies between the foliations of the forward and backward escaping sets), which we analyze in a broader, non-perturbative context.