Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics (Frontiers in Mathematics) (Paperback)

Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics (Frontiers in Mathematics) By Vladimir Dragovic, Milena Radnovic Cover Image
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Description


The goal of the book is to present, in a complete and comprehensive way, a few areas of mathematics interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. Most important results and ideas connected to Poncelet theorem are presented: classical as well as modern ones, together with historical overview with analysis of classical ideas, their natural generalizations, and natural generalizations. Special attention is payed to realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding of higher-dimensional analogues of Poncelet problems and realization of synthetic approach of higher genus addition theorems. This problem is realized in a sequence of papers of the authors, published in last 20 years. Some of those results represent the key contribution to the development of the theory, while this book gives the complete image.


Product Details
ISBN: 9783034800143
ISBN-10: 3034800142
Publisher: Birkhauser
Publication Date: May 6th, 2011
Pages: 294
Language: English
Series: Frontiers in Mathematics