On the definition of SRB-measures for coupled map lattices
The authors discuss the different definitions of SRB-measures that have been used in the literature. They show that unlikely for expanding maps on compact manifolds and other nice finite-dimensional systems, the different definitions of SRB-measures in the infinite-dimensional setting are not equivalent and do not give necessarilly an unique measure. For the infinite-dimensional setting the authors define SRB-measures as those having finite-dimensional projections that are absolutely continuous with respect to the corresponding Lebesgue measure. They construct a couple map lattice that exhibits an infinite number of such measures. They show that the multiplicity of SRB-measures exhibited on this example is not a rare behavior. In fact they argue that coupled maps lattices which are closed to an uncoupled expanding map have typically an infinite number of SRB-measures.
scientific article; zbMATH DE number 1742836