  Characterizing accurately chaotic behaviors is not a trivial problem and must
allow to determine the properties that two given chaotic invariant sets share
or not. The underlying problem is the classification of chaotic regimes, and
their labelling. Addressing these problems correspond to the development of a
dynamical taxonomy, exhibiting the key properties discriminating the variety of
chaotic behaviors discussed in the abundant literature. Starting from the
hierarchy of chaos initially proposed by one of us, we systematized the
description of chaotic regimes observed in three- and four-dimensional spaces,
which cover a large variety of known (and less known) examples of chaotic
systems. Starting with the spectrum of Lyapunov exponents as the first
taxonomic ranks, we extended the description to higher ranks with some concepts
inherited from topology (bounding torus, surface of section, first-return
map...).
  By treating extensively the R\"ossler and the Lorenz attractors, we extended
the description of branched manifold -- the highest taxonomic rank for
classifying chaotic attractor -- by a linking matrix (or linker) to
multi-component attractors (bounded by a torus whose genus g <= 3
