Discrete Integrable Systems: QRT Maps and Elliptic Surfaces (Springer Monographs in Mathematics) by J.J. Duistermaat

Discrete Integrable Systems: QRT Maps and Elliptic Surfaces (Springer Monographs in Mathematics)



Download Discrete Integrable Systems: QRT Maps and Elliptic Surfaces (Springer Monographs in Mathematics)




Discrete Integrable Systems: QRT Maps and Elliptic Surfaces (Springer Monographs in Mathematics) J.J. Duistermaat
Language: English
Page: 649
Format: pdf
ISBN: 1441971165, 9780387729237
Publisher: Springer

From the reviews: “This is an excellent book for graduates and researchers who have some knowledge of integrable systems and a rudimentary understanding of algebraic geometry. … Overall, this book delivers an excellent overview of a geometric interpretation of this class of discrete integrable systems, and is written in a manner that is fairly accessible to a postgraduate student or keen researcher in integrable systems.” (C. M. Ormerod, G. R. W. Quispel and J. A. G. Roberts, SIAM Review, Vol. 54 (1), 2012) 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, posing the question of determining the behavior of the discrete dynamical system defined by the iterates of the map. The aim of this book is to give a complete treatment not only of the basic facts about QRT maps, but also the background theory on which these maps are based. Readers with a good knowledge of algebraic geometry will be interested in Kodaira’s theory of elliptic surfaces and the collection of nontrivial applications presented here. While prerequisites for some readers will demand their knowledge of quite a bit of algebraic- and complex analytic geometry, different categories of readers will be able to become familiar with any selected interest in the book without having to make an extensive journey through the literature. MORE EBOOKS:
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