  The Earth's climate has experienced numerous critical transitions during its
history, which have often been accompanied by massive and rapid changes in the
biosphere. Such transitions are evidenced in various proxy records covering
different timescales. The goal is then to identify, date, and rank past
critical transitions in terms of importance, thus possibly yielding a more
thorough perspective on climatic history. To illustrate such an angle, which
inspired the punctuated equilibrium angle on the theory of evolution, we have
analyzed 2 key high-resolution datasets: the CENOGRID marine compilation (past
66 Myr), and North Atlantic U1308 record (past 3.3 Myr). By combining
recurrence analysis of the individual time series with a multivariate
representation of the system based on the theory of the quasi-potential, we
identify the key abrupt transitions associated with major regime changes that
differentiate various clusters of climate variability. This allows interpreting
the time-evolution of the system as a trajectory taking place in a dynamical
landscape, whose multiscale features are associated with a hierarchy of tipping
points.
