  We study the behavior of dynamical systems under time reparameterizations,
which is important not only to characterize chaos in relativistic systems but
also to probe the invariance of dynamical quantities. We first show that time
transformations are locally equivalent to metric transformations, a result that
leads to a transformation rule for all Lyapunov exponents on arbitrary
Riemannian phase spaces. We then show that time transformations preserve the
spectrum of generalized dimensions D_q except for the information dimension
D_1, which, interestingly, transforms in a nontrivial way despite previous
assertions of invariance. The discontinuous behavior at q=1 can be used to
constrain and extend the formulation of the Kaplan-Yorke conjecture.
