The intrinsic stochasticity of near-integrable Hamiltonian systems

Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolgomorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem is discussed and some numerical experiments on related astrophysical and high-temperature plasma problems are described.