Unidirectionally coupled interval maps: between dynamics and statistical mechanics (Q2782710)

The authors study coupled interval maps on the lattice \(\mathbb{N}^d\) where the coupling is unidirectional and sufficiently weak. For the single maps it is assumed that they are piecewise \(C^2\) expanding and stably satisfy a Lasota-Yorke inequality. NEWLINENEWLINENEWLINEThe authors focus on the class of probability measures for which all finite-dimensional conditional distributions are absolutely continuous with respect to the corresponding finite-dimensional Lebesgue measures. Using properties of Perron-Frobenius operators and a probabilistic coupling procedure for nonautonomous factors of the interacting system the authors show that two measures from this class are different if and only if their restriction to the spatial tail field differ. NEWLINENEWLINENEWLINEIn the case of a one-dimensional lattice \(\mathbb{N}\) with superexponentially decaying interaction such a measure is unique. Moreover, in this case exponential spatiotemporal mixing holds.