Marchuk N. The invariant tori for countable systems of difference equations with deviations of the discrete argument

This thesis is dedicated to creations of the basis for the theory of invariant toroidal manifolds for countable systems of linear and non-linear difference equations which are defined on finite-dimensional or infinite-dimensional tori and contain independent deviations of discrete argument. The principal problem here is the study of questions of the existence and smoothness of those manifolds. Sufficient conditions are presented for the existence and continuous differentiability by Freche of the invariant tori for linear, quasi-linear and non-linear systems which are defined on infinite-dimensional tori and contain the parameter from the space of bounded number sequences and independent deviations of the discrete argument.