Discrete Integrable Systems QRT Maps and Elliptic Surfaces /

• Main Author: Duistermaat, J.J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Edition: 1.
• Series: Springer Monographs in Mathematics, 304
• Subjects: Mathematics.; Geometry, algebraic.; Functions of complex variables.; Number theory.; Algebraic Geometry.; Functions of a Complex Variable.; Theoretical, Mathematical and Computational Physics.; Number Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-72923-7

The rich subject matter in this book brings in mathematics from different domains, especially from the theory of elliptic surfaces and dynamics.The material comes from the authors insights and understanding of a birational transformation of the plane derived from a discrete sine-Gordon equation, po...

Table of Contents:

• 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.