  Concepts from the Ergodic Theory are used to describe the existence of
non-transitive maps in attractors of phase synchronous chaotic systems. It is
shown that for a class of phase-coherent systems, e.g. the sinusoidally forced
Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization
implies that such maps exist. These ideas are also extended to other coupled
chaotic systems. In addition, a phase for a chaotic attractor is defined from
the tangent vector of the flow. Finally, it is discussed how these maps can be
used to real time detection of phase synchronization in experimental systems.
