Abstract
CONTENTS Introduction Chapter I. Integrable Lagrange systems with discrete time § 1. Hamiltonian theory of Lagrange systems with discrete time § 2. Discrete analogues of classical integrable systems and factorization of matrix polynomials § 3. Spectral theory of difference operators and discrete systems Chapter II. Integrability in dynamics of general algebraic maps § 1. Commuting polynomial maps and simple Lie groups § 2. Integrable polynomial automorphisms of the plane § 3. Algebraic relations and the Yang-Baxter equation. The growth of the number of images of iterations of multivalued maps References
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