Discrete Integrable Systems: QRT Maps and Elliptic Surfaces by J.J. Duistermaat PDF

By J.J. Duistermaat

This e-book is dedicated to Quisped, Roberts, and Thompson (QRT) maps, regarded as automorphisms of rational elliptic surfaces. the idea of QRT maps arose from difficulties in mathematical physics, related to distinction equations. the appliance of QRT maps to those and different difficulties within the literature, together with Poncelet mapping and the elliptic billiard, is tested intimately. The hyperlink among elliptic fibrations and fully integrable Hamiltonian structures can also be discussed.

The ebook starts with a accomplished review of the topic, together with QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, motion on homology periods, and periodic QRT maps. Later chapters disguise those issues and extra in detail.

While QRT maps may be prevalent to experts in algebraic geometry, the current quantity makes the topic obtainable to mathematicians and graduate scholars in a school room surroundings or for self-study.

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

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