This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, consideredas automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible tomathematicians and graduate students in a classroom setting or for self-study. Makes the theory of QRT maps accessible to non-specialists in algebraic geometry May be used as introduction to the theory of general elliptic surfaces Applies theory to Poncelet mappings, the elliptic billiard, and difference equations from mathematical physics Almost everything can be explicitly computed INDICE: Introduction.- The QRT Map.- Complex Projective Curves.- The QRT Surface.- Pencils of Cubic Curves in the Projective Plane.- The Action of the QRT Map on Homology Classes.- Elliptic Surfaces.- Rational Elliptic Surfaces.- Examples from the Literature.- Appendices.- Index.
- ISBN: 978-1-4419-7116-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 620
- Fecha Publicación: 29/08/2010
- Nº Volúmenes: 1
- Idioma: Inglés
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