  This work uses the statistical properties of Finite-Time Lyapunov Exponents
(FTLEs) to investigate the Intermittent Stickiness Synchronization (ISS)
observed in the mixed phase space of high-dimensional Hamiltonian systems. Full
Stickiness Synchronization (SS) occurs when all FTLEs from a chaotic trajectory
tend to zero for arbitrary long time-windows. This behavior is a consequence of
the sticky motion close to regular structures which live in the
high-dimensional phase space and affects all unstable directions proportionally
by the same amount, generating a kind of collective motion. Partial SS occurs
when at least one FTLE approaches to zero. Thus, distinct degrees of partial SS
may occur, depending on the values of nonlinearity and coupling parameters, on
the dimension of the phase space and on the number of positive FTLEs. Through
filtering procedures used to precisely characterize the sticky motion, we are
able to compute the algebraic decay exponents of the ISS and to obtain
remarkable evidence about the existence of a universal behavior related to the
decay of time correlations encoded in such exponents. In addition, we show that
even though the probability to find full SS is small compared to partial SSs,
the full SS may appear for very long times due to the slow algebraic decay of
time correlations in mixed phase space. In this sense, observations of very
late intermittence between chaotic motion and full SSs become rare events.
