Abstract of Paper

Periodicity and transitivity for cellular automata in Besicovitch topologies
by F. Blanchard, J. Cervelle and E. Formenti

Abstract:

We study cellular automata (CA) behavior in Besicovitch topology.
We solve an open problem about the existence of transitive CA.
The proof of this result has some interest in its own since it
is obtained by using Kolmogorov complexity. At our knowledge it
if the first result on discrete dynamical systems obtained
using Kolmogorov complexity. 
We also prove that every CA (in Besicovitch topology) either 
has a unique fixed point or a countable set of periodic points.
This result underlines that CA have a great degree of stability
and may be considered a further step towards the understanding
of CA periodic behavior.