Abstract: 10.1007/978-1-4419-9126-3 Copyright owner: Springer Science+Buisness Media, LLC, 2010 Data set: Springer Source Springer Monographs in Mathematics 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 authorâ€TMs 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 Kodairaâ€TMs 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 algebraicand complex analytic geometry, different categories of readers... more Identifiers series ISSN : 1439-7382 ISBN 978-1-4419-7116-6 e-ISBN 978-1-4419-9126-3 DOI Authors Additional information Publisher Springer New York book Read online Download Add to read later Add to collection Add to followed Share Export to bibliography J.J. Duistermaat Utrecht University, Department of Mathematics, Utrecht, Netherlands Terms of service Accessibility options Report an error / abuse © 2015 Interdisciplinary Centre for Mathematical and Computational Modelling Discrete integrable systems independent: it neither relies on nor used in the proof of integrability. Section 6 is not used in the proof of integrability. It discusses more specic discrete cluster integrable systems, assuming Theorem 3.7. Proof of part i) Take a pair of matchings (M1, M2) on Î“. Let us assign to them another pair of matchings (M1, M2) on Î“. Observe that [M1] âˆ’ [M2] is a 1-cycle.
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