Discrete integrable systems : QRT maps and elliptic surfaces
著者
書誌事項
Discrete integrable systems : QRT maps and elliptic surfaces
（Springer monographs in mathematics）
Springer, c2010
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注記
References: p. 613-620
Includes index
内容説明・目次
内容説明
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as 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 to mathematicians and graduate students in a classroom setting or for self-study.
目次
The QRT Map.- The Pencil of Biquadratic Curves in .- The QRT surface.- Cubic Curves in the Projective Plane.- The Action of the QRT Map on Homology.- Elliptic Surfaces.- Automorphisms of Elliptic Surfaces.- Elliptic Fibrations with a Real Structure.- Rational elliptic surfaces.- Symmetric QRT Maps.- Examples from the Literature.- Appendices.
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