  The study of chaos in relativistic systems has been hampered by the observer
dependence of Lyapunov exponents (LEs) and of conditions, such as orbit
boundedness, invoked in the interpretation of LEs as indicators of chaos. Here
we establish a general framework that overcomes both difficulties and apply the
resulting approach to address three fundamental questions: how LEs transform
under Lorentz and Rindler transformations and under transformations to
uniformly rotating frames. The answers to the first and third questions show
that inertial and uniformly rotating observers agree on a characterization of
chaos based on LEs. The second question, on the other hand, is an ill-posed
problem due to the event horizons inherent to uniformly accelerated observers.
