  We compute Lyapunov spectra for Coulombic and gravitational versions of the
one-dimensional systems of parallel sheets with periodic boundary conditions.
Exact time evolution of tangent-space vectors are derived and are utilized
toward computing Lypaunov characteristic exponents using an event-driven
algorithm. The results indicate that the energy dependence of the largest
Lyapunov exponent emulates that of Kolmogorov-entropy density for each system
at different degrees of freedom. Our approach forms an effective and
approximation-free tool toward studying the dynamical properties exhibited by
the Coulombic and gravitational systems and finds applications in investigating
indications of thermodynamic transitions in large versions of the spatially
periodic systems.
