On mechanisms of destruction of adiabatic invariance in slow-fast Hamiltonian systems

In many problems of classical mechanics and theoretical physics dynamics can be described as a slow evolution of periodic or quasi-periodic processes. Adiabatic invariants are approximate first integrals for such dynamics. The existence of adiabatic invariants makes dynamics close to regular. Destruction of adiabatic invariance leads to chaotic dynamics. We present a review of some mechanisms of destruction of adiabatic invariance in slow–fast Hamiltonian systems with examples from charged particle dynamics.