Discrete Integrable Systems

This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Includes supplementary material: sn.pub/extras

Inhalt
Three Lessons on the Painlevé Property and the Painlevé Equations (M.D. Kruskal, B. Grammaticos, T. Tamizhmani).- Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems (R. Willox, J. Satsuma).- Special Solutions of Discrete Integrable Systems (Y. Ohta).- Discrete Differential Geometry. Integrability as Consistency (A.I. Bobenko).- Discrete Lagrangian Models (Yu.B. Suris).- Symmetries of Discrete Systems (P. Winternitz).- Discrete Painlevé Equations: A Review (B. Grammaticos, A. Ramani).- Special Solutions for Discrete Painlevé Equations (K.M. Tamizhmani, T. Tamizhmani, B. Grammaticos, A. Ramani).- Ultradiscrete Systems (Cellular Automata) (T. Tokihiro).- Time in Science: Reversibility vs. Irreversibility (Y. Pomeau).