Application of Bernoulli shift to investigation of stability of spatially periodic solutions in lattice dynamical systems

摘要

We consider lattice dynamical systems in the space B of bi-infinite sequences of vectors equipped by the supremum norm. Using the general result about the spectrum of certain operators on powers of a Banach space applied to Bernoulli shift, we are able to determine the spectrum of certain linear operators on B. This enables us to decide about the stability of spatially homogeneous or spatially periodic solutions of the considered lattice dynamical system.