Orbits of nearly integrable systems accumulating to KAM tori

Marcel Guardia, Vadim Kaloshin

Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \[ H_ε(φ,I,t)=H_0(I)+εH_1(φ,I,t), φ\in T^2,\ I\…