Nonlinear Dynamics and Chaos in Many-Particle Hamiltonian Systems

We report the results of studies of nonlinear dynamics and dynamical chaos in Hamiltonian systems composed of many interacting particles. The importance of the Lyapunov exponents and the Kolmogorov-Sinai entropy is discussed in the context of ergodic theory and nonequilibrium statistical mechanics. Two types of systems are studied: hard-ball models for the motion of a tracer or Brownian particle interacting with the particles of a surrounding fluid and microplasmas which are composed of positively charged ions confined in a Penning electromagnetic trap. Lyapunov exponents are studied for both classes of systems. In microplasmas, transitions between different regimes of nonlinear behavior and chaos are reported.