Book contents
- Frontmatter
- Contents
- List of figures
- List of contributors
- Preface
- Introduction
- 1 Lagrangian and Hamiltonian Formalism for Discrete Equations: Symmetries and First Integrals
- 2 Painlevé Equations: Continuous, Discrete and Ultradiscrete
- 3 Definitions and Predictions of Integrability for Difference Equations
- 4 Orthogonal Polynomials, their Recursions, and Functional Equations
- 5 Discrete Painlevé Equations and Orthogonal Polynomials
- 6 Generalized Lie Symmetries for Difference Equations
- 7 Four Lectures on Discrete Systems
- 8 Lectures on Moving Frames
- 9 Lattices of Compact Semisimple Lie Groups
- 10 Lectures on Discrete Differential Geometry
- 11 Symmetry Preserving Discretization of Differential Equations and Lie Point Symmetries of Differential-Difference Equations
Preface
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- Contents
- List of figures
- List of contributors
- Preface
- Introduction
- 1 Lagrangian and Hamiltonian Formalism for Discrete Equations: Symmetries and First Integrals
- 2 Painlevé Equations: Continuous, Discrete and Ultradiscrete
- 3 Definitions and Predictions of Integrability for Difference Equations
- 4 Orthogonal Polynomials, their Recursions, and Functional Equations
- 5 Discrete Painlevé Equations and Orthogonal Polynomials
- 6 Generalized Lie Symmetries for Difference Equations
- 7 Four Lectures on Discrete Systems
- 8 Lectures on Moving Frames
- 9 Lattices of Compact Semisimple Lie Groups
- 10 Lectures on Discrete Differential Geometry
- 11 Symmetry Preserving Discretization of Differential Equations and Lie Point Symmetries of Differential-Difference Equations
Summary
This book is based upon lectures delivered during the Summer School on Symmetries and Integrability of Difference Equations at the Université de Montréal, Canada, June 8, 2008–June 21, 2008. The lectures are devoted to methods that have been developed over the last 15–20 years for discrete equations. They are based on either the inverse spectral approach or on the application of geometric and group theoretical techniques. The topics covered in this volume can be summarized in the following categories:
Integrability of difference equations
Discrete differential geometry
Special functions and their relation to continuous and discrete Painlevé functions
Discretization of complex analysis
General aspects of Lie group theory relevant for the study of difference equations. Specifically, two such subjects are treated: 1. Cartan's method of moving frames 2. Lattices in Euclidean space, symmetrical under the action of semisimple Lie groups
Lie point symmetries and generalized symmetries of discrete equations
Twelve distinct lecture series were presented at the Summer School of which eleven are included in this volume. Close to 50 registered graduate students and researchers from twelve different countries participated.
The Summer School, Séminaire de mathématiques supérieures, is a yearly event at the Département de Mathématiques, Université de Montréal. The organizing committee for the year 2008 consisted of Pavel Winternitz (Université de Montréal, Canada), Vladimir Dorodnitsyn (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences), Decio Levi (Università degli Studi Roma Tre, Italy) and Peter Olver (University of Minnesota, USA).
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- Information
- Symmetries and Integrability of Difference Equations , pp. xvii - xviiiPublisher: Cambridge University PressPrint publication year: 2011