  A recently introduced chaos detection method, the Relative Lyapunov Indicator
(RLI) is investigated in the cases of symplectic mappings and continuous
Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in
determining the true nature of individual orbits, and in separating ordered and
chaotic regions of the phase space of dynamical systems. A comparison between
the RLI and some other variational indicators are presented, as well as the
recent applications of the RLI to various problems of dynamical astronomy.
