Discrete Integrable Systems QRT Maps and Elliptic Surfaces /

• Main Author: Duistermaat, J.J (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Edition: 1.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebraic geometry.; Functions of complex variables.; Number theory.; Physics.; Algebraic Geometry.; Functions of a Complex Variable.; Theoretical, Mathematical and Computational Physics.; Number Theory.

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 author’s insights and understanding of a birational transformation of the plane derived from a discrete sine-Gordon equation, po...

Table of Contents:

• 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. .