Can the shape of attractor forbid chaotic phase synchronization?

We address the question, which properties of a chaotic oscillator are crucial for its ability/inability to synchronize with external force or other similar oscillators. The decisive role is played by temporal coherency whereas the shape of the attractor is less important. We discuss the role of coordinate-dependent reparameterizations of time which preserve the attractor geometry but greatly influence the coherency. An appropriate reparameterization enables phase synchronization in coupled multiscroll attractors. In contrast, the ability to synchronize phases for nearly isochronous oscillators can be destroyed by a reparameterization which washes out the characteristic time scale.