Onset of Dynamical Chaos: Mathematical Aspects
The theory of chaos originated in the works by H. Poincaré is related to the problem of integrability of Hamiltonian systems under small periodic perturbations, i.e., to the fundamental problem of dynamics (see, Sect. 6.2.1). Chaos of magnetic field lines in magnetic fusion devices is an excellent example of dynamical chaos in Hamiltonian systems with one-and-half-degrees of freedom. In this chapter we discuss the some mathematical aspects of the onset of chaos in Hamiltonian systems.