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
Citation:
Gelfreich V. G., Turaev D. V., Universal dynamics in a neighborhood of a generic elliptic periodic point, Regular and Chaotic Dynamics,
2010, Volume 15, Numbers 2-3,
pp. 159-164