The Zeldovich approximation: key to understanding Cosmic Web complexity
  We describe how the dynamics of cosmic structure formation defines the
intricate geometric structure of the spine of the cosmic web. The Zeldovich
approximation is used to model the backbone of the cosmic web in terms of its
singularity structure. The description by Arnold et al. (1982) in terms of
catastrophe theory forms the basis of our analysis.
  This two-dimensional analysis involves a profound assessment of the
Lagrangian and Eulerian projections of the gravitationally evolving
four-dimensional phase-space manifold. It involves the identification of the
complete family of singularity classes, and the corresponding caustics that we
see emerging as structure in Eulerian space evolves. In particular, as it is
instrumental in outlining the spatial network of the cosmic web, we investigate
the nature of spatial connections between these singularities.
  The major finding of our study is that all singularities are located on a set
of lines in Lagrangian space. All dynamical processes related to the caustics
are concentrated near these lines. We demonstrate and discuss extensively how
all 2D singularities are to be found on these lines. When mapping this spatial
pattern of lines to Eulerian space, we find a growing connectedness between
initially disjoint lines, resulting in a percolating network. In other words,
the lines form the blueprint for the global geometric evolution of the cosmic
web.
