RESUMEN
The chaotic phase synchronization transition is studied in connection with the zero Lyapunov exponent. We propose a hypothesis that it is associated with a switching of the maximal finite-time zero Lyapunov exponent, which is introduced in the framework of a large deviation analysis. A noisy sine circle map is investigated to introduce this hypothesis and it is tested in an unidirectionally coupled Rössler system by using the covariant Lyapunov vector associated with the zero Lyapunov exponent.
RESUMEN
We propose a level dynamics approach to the large deviation statistical characteristic function phi(q) for temporal series of dynamical variable V, which is the largest eigenvalue of the generalized evolution operator H{q}(identical with H+qV). This is done first by deriving "equations of motion" for the eigenvalues and the eigenstates of H{q} with the initial conditions determined by those of H , the true evolution operator for the dynamical variable under consideration, and then by solving these equations. Furthermore, utilizing simple solvable models, it is shown that the eigenvalues and eigenstates satisfy the equations of motion derived in this paper.
