  The goal of this paper is twofold. In the first part we discuss a general
approach to determine Lyapunov exponents from ensemble- rather than
time-averages. The approach passes through the identification of locally stable
and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy
with generalized synchronization. The method is then applied to a periodically
forced chaotic oscillator to show that the modulus of the Lyapunov exponent
associated to the phase dynamics increases quadratically with the coupling
strength and it is therefore different from zero already below the onset of
phase-synchronization. The analytical calculations are carried out for a model,
the generalized special flow, that we construct as a simplified version of the
periodically forced Rossler oscillator.

Chaotic Dynamics