CRM Proceedings & Lecture Notes 2000; 444 pp; softcover Volume: 25 ISBN10: 0821821288 ISBN13: 9780821821282 List Price: US$114 Member Price: US$91.20 Order Code: CRMP/25
 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 equationsoften referred to more generally as discrete systemshas undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lietype symmetries of differentialdifference and differencedifference 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 Painlevé equations, difference and qdifference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discretetime 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. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students in mathematics and theoretical physics; researchers in mathematics, physics and informatics. Reviews "Strongly recommend this volume to all libraries of research institutions and to mathematicians with interest in difference equations."  CMS Notes Table of Contents  M. S. Alber, R. Camassa, and M. Gekhtman  Billiard weak solutions of nonlinear PDE's and Toda flows
 N. M. Atakishiyev  FourierGauss transforms of some \(q\)spectral functions
 M. Błaszak and A. Szum  Integrable differentialdifference systems in (2 + 1)dimensions and their Hamiltonian structure
 L. V. Bogdanov and B. G. Konopelchenko  Möbius invariant integrable lattice equations associated with the generalized KP hierarchy
 M. Boiti, F. Pempinelli, A. K. Pogrebkov, and B. Prinari  Wave soliton solutions on a generic background for KPI equation
 C. Brezinski  Difference and differential equations and convergence acceleration algorithms
 A. S. Cârstea  On the dynamics of rational solutions for 1D Volterra system
 C. Cresswell  Monodromy data for the discrete first Painlevé hierarchy
 G. Dattoli  Differential identities, generalized polynomials and applications in physics and mathematics
 A. Doliwa  Lattice geometry of the Hirota equation
 A. Doliwa and P. M. Santini  Integrable discrete geometry: The quadrilateral lattice, its transformations and reductions
 J. C. Eilbeck, V. Z. Enolskii, and D. V. Leykin  On the Kleinian construction of abelian functions of canonical algebraic curves
 P. G. Estévez and P. A. Clarkson  Discrete equations and the singular manifold method
 Yu. Fedorov  Discrete versions of some algebraic integrable systems related to generalized Jacobians
 M. L. Gandarias  New potential symmetries
 D. G. Oteiza, S. Lafortune, and P. Winternitz  Symmetry classification of systems of differentialdifference equations
 I. T. Habibullin and A. N. Vil'danov  Integrable boundary conditions for nonlinear lattices
 J. Harnad and J. McKay  Modular invariants and generalized Halphen systems
 R. H. Heredero, D. Levi, and P. Winternitz  Symmetry preserving discretization of the Burgers equation
 J. Hietarinta and C. Viallet  Singularity confinement and degree growth
 R. Hirota and M. Iwao  Timediscretization of soliton equations
 A. N. W. Hone, V. B. Kuznetsov, and O. Ragnisco  Bäcklund transformations for the HénonHeiles and Garnier systems
 N. Joshi  Irregular singular behaviour in the first discrete Painlevé equation
 N. A. Kudryashov and A. Pickering  Rational and special solutions of the \(P_{\mathrm{II}}\) hierarchy
 S. Lafortune, B. Grammaticos, and A. Ramani  Linearisable systems and the Gambier approach
 W. Lay  Difference equations of PoincaréPerron type and central twopoint connection problems
 I. Loutsenko and V. Spiridonov  Selfsimilarity in spectral problems and \(q\)special functions
 L. Martina  Lie point symmetries of discrete and continual SU(\(\infty\)) Toda field theory
 K.i. Maruno, K. Kajiwara, and M. Oikawa  A note on integrable systems related to discrete time Toda lattice
 T. Miwa and Y. Takeyama  The integral formula for the solutions of the quantum KnizhnikZamolodchikov equation associated with \(U_q(\widehat{sl}_n)\) for \(q = 1\)
 L. M. Nieto, J. Negro, F. J. Herranz, and A. Ballesteros  Symmetries of the discrete Schrödinger equation and its quantum deformations
 Y. Ohta  Determinant and Pfaffian solutions for discrete soliton equations
 V. G. Papageorgiou  Difference isomonodromy problems and discrete Painlevé equations
 A. P. Protogenov and V. A. Verbus  Discrete equations of motion for \(A_{k1}\) algebra
 G. R. W. Quispel and D. Levi  Discrete Painlevé equations from nonisospectral soliton equations
 A. Ramani, B. Grammaticos, and S. Lafortune  A study of the continuous and discrete Gambier systems
 W. K. Schief and B. G. Konopelchenko  Discrete surfaces of revolution
 M. Senthilvelan  KacMoodyVirasoro algebras and integrability of certain higher dimensional nonlinear evolutionary equations
 A. Turbiner  Different faces of harmonic oscillator
 W. Van Assche  Nonsymmetric linear difference equations for multiple orthogonal polynomials
 V. L. Vereschagin  Asymptotics for solution to the Cauchy problem for Volterra lattice with steplike initial values
 C. Viallet  Complexity and integrability
