Vered Rom-Kedar (Weizmann Institute)
Abstract: Hamiltonian impact systems combine smooth Hamiltonian motion with elastic reflections from boundaries, providing a natural setting for studying the interplay between integrability, singularities, and perturbations.
After briefly recalling how steep smooth potentials approximating hard impacts can generate KAM stability islands, even in systems with many degrees of freedom (joint work with D. Turaev), I will focus on nearly pseudo-integrable Hamiltonian impact systems (joint works with I. Pazi, A. Zobova and S. Tanny).
For separable Hamiltonians with rectilinear impact boundaries, the invariant surfaces may have higher genus, and the dynamics are conjugate to directional flows on translation surfaces. Consequently, iso-energy return maps form families of interval exchange transformations rather than rotations.
I will describe how small perturbations give rise to reversible, piecewise-smooth area-preserving maps, and how time-reversal symmetry governs the persistence and bifurcations of periodic orbits. Near the transition from rotations to interval exchanges, these maps exhibit hovering orbits: trajectories that repeatedly pass above and beside a step-shaped barrier without ever colliding with it.