ANALYTICAL APPROACH FOR PIECEWISE-LINEAR COUPLED MAP LATTICES

A simple construction is presented which generalizes piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in th e mathematical literature, allows for an analytical investigation. In particular, the spin Hamiltonian which is generated by the symbolic dy namics is accessible. As an example, a formal relation between a globa lly coupled system and an Ising mean-field model is established. The p hase transition in the limit of infinite system size is analyzed and a nalytical results are compared with numerical simulations.