We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these innnite dimensional dynamical systems which exhibits space-time-chaos.

We consider a collection of n points in R measured at m times, which are encoded in an n × d × m data tensor. Our objective is to define a single embedding of the n points into Euclidean space which summarizes the geometry as described by the data tensor. In the case of a fixed data set, diffusion maps (and related graph Laplacian methods) define such an embedding via the eigenfunctions of a di...

Abstract We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stab...