On degenerate resonances in Hamiltonian systems with two degrees of freedom

For Hamiltonian systems with two degrees of freedom close to nonlinear integrable, notations of a degenerate resonance and an order of degeneracy n   are introduced along with a local normal form near the resonance. Based on an averaged system, bifurcations in zones of degenerate resonances are studied. For n=3n=3 (continuing the well-studied case n=2n=2), generic bifurcations of equilibria, separatrix reconnections, occurrence of meander curves and Kármán vortex streets are revealed and discussed.