Critical Locus for Complex Henon maps.
For one dimensional maps, the dynamics of the map is too large extent determined by the orbits of the critical points. Complex Henon maps are automorphisms, and as such do not have critical points. Critical loci, sets of tangencies between dynamically defined foliations/laminations often serve as a good analog of the critical points. We study the critical loci in the escape region, defined by Bedford, Smillie and Hubbard. The critical locus in this region is a one-dimensional analytic set. We'll discuss the relation between the dynamical properties of the map and topological properties of the critical locus. We will give a description of the critical locus for Henon maps in HOV region. This is a joint work in progress with Remus Radu and Raluca Tanase.