  We provide appropriate tools for the analysis of dynamics and chaos for
one-dimensional systems with periodic boundary conditions. Our approach allows
for the investigation of the dependence of the largest Lyapunov exponent on
various initial conditions of the system. The method employs an effective
approach for defining the phase-space distance appropriate for systems with
periodic boundary and allows for an unambiguous test-orbit rescaling in the
phase space required to calculate the Lyapunov exponents. We elucidate our
technique by applying it to investigate the chaotic dynamics of a
one-dimensional plasma with periodic boundary. Exact analytic expressions are
derived for the electric field and potential using Ewald sums thereby making it
possible to follow the time-evolution of the plasma in simulation without any
special treatment of the boundary. By employing a set of event-driven
algorithms, we calculate the largest Lyapunov exponent, the radial distribution
function and the kinetic pressure by following the evolution of the system in
phase space without resorting to numerical manipulation of the equations of
motion. Simulation results are presented and analyzed for the one-dimensional
plasma with a view to examining the dynamical and chaotic behavior exhibited by
small and large versions of the system.
