Symmetries & Integrability of Difference Equations by Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz
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About this book :-
Symmetries & Integrability of Difference Equations written by
Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz .
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
(Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz)
Book Detail :-
Title: Symmetries & Integrability of Difference Equations
Edition:
Author(s): Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz
Publisher: Cambridge University Press
Series: London Mathematical Society Lecture Note Series 381
Year: 2011
Pages: 360
Type: PDF
Language: English
ISBN: 052113658X,9780521136587
Country: US
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About Author :-
The author Peter J. Olver is an American mathematician whose primary research interests involve the applications of symmetry and Lie groups to differential equations. He has been a full professor at the University of Minnesota since 1985 and is currently head of their mathematics department. In 2003, Olver was one of the top 234 most cited mathematicians in the world.
In 2014, Olver became a fellow of the Society for Industrial and Applied Mathematics for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.". In addition, Olver is an elected fellow of the Institute of Physics and a fellow of the American Mathematical Society.
Olver is a prolific author, having written over 200 academic papers as of 2015. Of these, 137 have appeared or will appear in major refereed journals, 46 have appeared in conference proceedings and seven have appeared as appendices and chapters in books.
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Book Contents :-
Symmetries & Integrability of Difference Equations written by
Decio Levi, Peter Olver, Zora Thomova, Pavel Winternitz
cover the following topics.
'
0. Introduction
1. Lagrangian and Hamiltonian Formalism for Discrete Equations: Symmetries and First Integrals V. Dorodnitsyn and R. Kozlov
2. Painlevé Equations: Continuous, Discrete and Ultradiscrete, B. Grammaticos and A. Ramani
3. Definitions and Predictions of Integrability for Difference, Equations J. Hietarinta
4. Orthogonal Polynomials, their Recursions, and Functional Equations M. E. H. Ismail
5. Discrete Painlevé Equations and Orthogonal Polynomials, A. Its
6. Generalized Lie Symmetries for Difference Equations, D. Levi and R. I. Yamilov
7. Four Lectures on Discrete Systems,S. P. Novikov
8. Lectures on Moving Frames P. J. Olver
9. Lattices of Compact Semisimple Lie Groups J. Patera
10. Lectures on Discrete Differential Geometry Yu. B Suris
11. Symmetry Preserving Discretization of Differential Equations and Lie Point Symmetries of Differential-Difference Equations, P. Winternitz
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