  Consider a $C^1$ vector field together with an ergodic invariant probability
that has $\ell$ nonzero Lyapunov exponents. Using orthonormal moving frames
along certain transitive orbits we construct a linear system of $\ell$
differential equations which is a reduced form of Liao's "standard system". We
show that the Lyapunov exponents of this linear system coincide with all the
nonzero exponents of the given vector field with respect to the given
probability. Moreover, we prove that these Lyapunov exponents have a
persistence property that implies that a "Liao perturbation" preserves both
sign and value of nonzero Lyapunov exponents.
