Stable and unstable dynamics in Hamiltonian Dynamical Systems
Dynamical Systems, Hamiltonian Dynamics, Singular perturbations, Separatrix splitting, Exponentially small asymptotics, bifurcation theory, normal forms
There is a remarkable similarity between bifurcations of equilibria of planar vector fields and fixed points of two-dimensional diffeomorphisms. A single normal form can be used to describe both of them. In this way any qualitative difference between these two different types of dynamical systems is moved beyond all algebraic orders.
The project is aimed on studying differences between these two types of bifurcations including the analytical mechanisms for divergence of normal forms and asymptotic estimates for width of chaotic zones.
Detection of exponentially small quantities requires studying the analytical continuation of a system into C2, and may be related to the theory of resurgent functions.