SIDE III: Symmetries and Integrability of Difference Equations(CRM Proceedings & Lecture Notes)

This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations-often referred to more generally as discrete systems-has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painleve equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.

Table of Contents:
Billiard weak solutions of nonlinear PDE's and Toda flows by M. S. Alber, R. Camassa, and M. Gekhtman Fourier-Gauss transforms of some $q$-spectral functions by N. M. Atakishiyev Integrable differential-difference systems in (2 + 1)-dimensions and their Hamiltonian structure by M. Blaszak and A. Szum Mobius invariant integrable lattice equations associated with the generalized KP hierarchy by L. V. Bogdanov and B. G. Konopelchenko Wave soliton solutions on a generic background for KPI equation by M. Boiti, F. Pempinelli, A. K. Pogrebkov, and B. Prinari Difference and differential equations and convergence acceleration algorithms by C. Brezinski On the dynamics of rational solutions for 1-D Volterra system by A. S. Carstea Monodromy data for the discrete first Painleve hierarchy by C. Cresswell Differential identities, generalized polynomials and applications in physics and mathematics by G. Dattoli Lattice geometry of the Hirota equation by A. Doliwa Integrable discrete geometry: The quadrilateral lattice, its transformations and reductions by A. Doliwa and P. M. Santini On the Kleinian construction of abelian functions of canonical algebraic curves by J. C. Eilbeck, V. Z. Enolskii, and D. V. Leykin Discrete equations and the singular manifold method by P. G. Estevez and P. A. Clarkson Discrete versions of some algebraic integrable systems related to generalized Jacobians by Yu. Fedorov New potential symmetries by M. L. Gandarias Symmetry classification of systems of differential-difference equations by D. G.-U. Oteiza, S. Lafortune, and P. Winternitz Integrable boundary conditions for nonlinear lattices by I. T. Habibullin and A. N. Vil'danov Modular invariants and generalized Halphen systems by J. Harnad and J. McKay Symmetry preserving discretization of the Burgers equation by R. H. Heredero, D. Levi, and P. Winternitz Singularity confinement and degree growth by J. Hietarinta and C. Viallet Time-discretization of soliton equations by R. Hirota and M. Iwao Backlund transformations for the Henon-Heiles and Garnier systems by A. N. W. Hone, V. B. Kuznetsov, and O. Ragnisco Irregular singular behaviour in the first discrete Painleve equation by N. Joshi Rational and special solutions of the $P_{\mathrm{II}}$ hierarchy by N. A. Kudryashov and A. Pickering Linearisable systems and the Gambier approach by S. Lafortune, B. Grammaticos, and A. Ramani Difference equations of Poincare-Perron type and central two-point connection problems by W. Lay Self-similarity in spectral problems and $q$-special functions by I. Loutsenko and V. Spiridonov Lie point symmetries of discrete and continual SU($\infty$) Toda field theory by L. Martina A note on integrable systems related to discrete time Toda lattice by K.-i. Maruno, K. Kajiwara, and M. Oikawa The integral formula for the solutions of the quantum Knizhnik-Zamolodchikov equation associated with $U_q(\widehat{sl}_n)$ for $|q| = 1$ by T. Miwa and Y. Takeyama Symmetries of the discrete Schrodinger equation and its quantum deformations by L. M. Nieto, J. Negro, F. J. Herranz, and A. Ballesteros Determinant and Pfaffian solutions for discrete soliton equations by Y. Ohta Difference isomonodromy problems and discrete Painleve equations by V. G. Papageorgiou Discrete equations of motion for $A_{k-1}$ algebra by A. P. Protogenov and V. A. Verbus Discrete Painleve equations from nonisospectral soliton equations by G. R. W. Quispel and D. Levi A study of the continuous and discrete Gambier systems by A. Ramani, B. Grammaticos, and S. Lafortune Discrete surfaces of revolution by W. K. Schief and B. G. Konopelchenko Kac-Moody-Virasoro algebras and integrability of certain higher dimensional nonlinear evolutionary equations by M. Senthilvelan Different faces of harmonic oscillator by A. Turbiner Nonsymmetric linear difference equations for multiple orthogonal polynomials by W. Van Assche Asymptotics for solution to the Cauchy problem for Volterra lattice with step-like initial values by V. L. Vereschagin Complexity and integrability by C. Viallet.

Review :
"Strongly recommend this volume to all libraries of research institutions and to mathematicians with an interest