  The study of dynamics in general relativity has been hampered by a lack of
coordinate independent measures of chaos. Here we present a variety of
invariant measures for quantifying chaotic dynamics in relativity by exploiting
the coordinate independence of fractal dimensions. We discuss how preferred
choices of time naturally arise in chaotic systems and how the existence of
invariant signals of chaos allow us to reinstate standard coordinate dependent
measures. As an application, we study the Mixmaster universes and find it to
exhibit transient soft chaos.
