ABSTRACT:

I report about a two-dimensional lattice of continuous, piecewise linear and expanding interval maps coupled to its nearest north and east neighbours, which has a unique SRB measure for weak coupling strength and which has at least two such invariant measures for stronger coupling. At the same time the corresponding systems on finite lattices always have a unique absolutely continuous SRB measure. The construction refers to Toom's probabilistic cellular automata. (Joint work with J.-B. Bardet)