  Topological dynamics of cellular automata (CA), inherited from classical
dynamical systems theory, has been essentially studied in dimension 1. This
paper focuses on 2D CA and aims at showing that the situation is different and
more complex. The main results are the existence of non sensitive CA without
equicontinuous points, the non-recursivity of sensitivity constants and the
existence of CA having only non-recursive equicontinuous points. They all show
a difference between the 1D and the 2D case. Thanks to these new constructions,
we also extend undecidability results concerning topological classification
previously obtained in the 1D case.
