LEADER 04515nam 22006135 450 001 9910254573103321 005 20220404194740.0 010 $a3-319-56666-0 024 7 $a10.1007/978-3-319-56666-5 035 $a(CKB)3710000001418540 035 $a(MiAaPQ)EBC4894904 035 $a(DE-He213)978-3-319-56666-5 035 $a(PPN)202991598 035 $a(EXLCZ)993710000001418540 100 $a20170630d2017 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aSymmetries and integrability of difference equations $electure notes of the Abecederian school of SIDE 12, Montreal 2016 /$fedited by Decio Levi, Raphaël Rebelo, Pavel Winternitz 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (435 pages) 225 1 $aCRM Series in Mathematical Physics 311 $a3-319-56665-2 320 $aIncludes bibliographical references and index. 327 $aChapter 1. Continuous, Discrete and Ultradiscrete Painlevé Equations -- Chapter 2. Elliptic Hypergeometric Functions -- Chapter 3. Integrability of Difference Equations through Algebraic Entropy and Generalized Symmetries -- Chapter 4. Introduction to Linear and Nonlinear Integrable Theories in Discrete Complex Analysis -- Chapter 5. Discrete Integrable Systems, Darboux Transformations and Yang?Baxter Maps -- Chapter 6. Symmetry-Preserving Numerical Schemes -- Chapter 7. Introduction to Cluster Algebras -- Chapter 8. An Introduction to Difference Galois Theory -- Chapter 9. Lectures on Quantum Integrability: Lattices, Symmetries and Physics. 330 $aThis book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers. 410 0$aCRM Series in Mathematical Physics 606 $aPhysics 606 $aDifference equations 606 $aFunctional equations 606 $aAlgebra 606 $aField theory (Physics) 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 615 0$aPhysics. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aAlgebra. 615 0$aField theory (Physics) 615 14$aNumerical and Computational Physics, Simulation. 615 24$aDifference and Functional Equations. 615 24$aField Theory and Polynomials. 676 $a515.35 702 $aLevi$b Decio$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aRebelo$b Raphaël$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aWinternitz$b Pavel$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910254573103321 996 $aSymmetries and integrability of difference equations$9242391 997 $aUNINA