Dmitrii Mints (Imperial): High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms

Our research is aimed at studying the dynamics of smooth multidimensional diffeomorphisms from Newhouse domain, that is, open regions in the space of maps where systems with homoclinic tangencies are dense. We prove that in the space of smooth and real-analytic multidimensional maps in any neighborhood of a map such that it has a bi-focus periodic orbit whose invariant manifolds are tangent, there exist open regions (which are subdomain of the Newhouse domain) where maps with high order homoclinic tangencies of corank-2 (invariant manifolds forming the tangency have a plane of common tangent vectors) are dense and maps having universal two-dimensional dynamics are residual.