Stable and unstable dynamics in Hamiltonian Dynamical Systems

### Research Interests

Dynamical Systems, Hamiltonian Dynamics, Singular perturbations,
Separatrix splitting, Exponentially small asymptotics, bifurcation
theory, normal forms

### Research Project:

Dynamics of Hamiltonian Systems with
multiple time scales

### Research Project:

Resonant Phenomena in Hamiltonian Systems

### Research Project:

Asymptotic beyond all orders and Stokes
phenomenon in bifurcation problems

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.