TY  - BOOK
AU  - Levi,D.
TI  - Symmetries and integrability of difference equations
T2  - London Mathematical Society lecture note series
SN  - 9780511997136 (ebook)
AV  - QA431 .S952 2011
U1  - 515/.625 22
PY  - 2011///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Difference equations
KW  - Symmetry (Mathematics)
KW  - Integrals
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Lagrangian and Hamiltonian formalism for discrete equations: symmetries and first integrals / V. Dorodnitsyn and R. Kozlov -- Painlevé equations: continuous, discrete and ultradiscrete / B. Grammaticos and A. Ramani -- Definitions and predictions of integrability for difference equations / J. Hietarinta -- Orthogonal polynomials, their recursions, and functional equations / M.E.H. Ismail -- Discrete Painlevé equations and orthogonal polynomials / A. Its -- Generalized Lie symmetries for difference equations / D. Levi and R.I. Yamilov -- Four lectures on discrete systems / S.P. Novikov -- Lectures on moving frames / P.J. Olver -- Lattices of compact semisimple Lie groups / J. Patera -- Lectures on discrete differential geometry / Yu. B Suris -- Symmetry preserving discretization of differential equations and Lie point symmetries of differential-difference equations / P. Winternitz
N2  - Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference
UR  - https://doi.org/10.1017/CBO9780511997136
ER  -