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

By J.J. Duistermaat

This ebook is dedicated to Quisped, Roberts, and Thompson (QRT) maps, regarded as automorphisms of rational elliptic surfaces. the speculation of QRT maps arose from difficulties in mathematical physics, regarding 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 platforms is additionally discussed.

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

While QRT maps might be ordinary to experts in algebraic geometry, the current quantity makes the topic available to mathematicians and graduate scholars in a school room atmosphere or for self-study.

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