Evolutionary equations are studied in abstract Banach spaces and in
spaces of bounded number sequences. For linear and nonlinear
difference equations, which are defined on finite-dimensional and
infinite-dimensional tori, the problem of reducibility is solved,
in particular, in neighborhoods of their invariant sets, and the
basics for a theory of invariant tori and bounded semi-invariant
manifolds are established. Also considered are the questions on
existence and approximate construction of periodic solutions for
difference equations in infinite-dimensional spaces and the problem
of extendibility of the solutions in degenerate cases. For
nonlinear differential equations in spaces of bounded number
sequences, new results are obtained in the theory of
countable-point boundary-value problems.The book contains new
mathematical results that will be useful towards advances in
nonlinear mechanics and theoretical physics.
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