Abstract:
We show that a generic area-preserving two-dimensional map with an elliptic periodic point is $C^\omega$-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.
Keywords:homoclinic tangency, wild hyperbolic set, Newhouse phenomenon, Hamiltonian system, area-preserving map, volume-preserving flow, exponentially small splitting, KAM theory.