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  • © 2011

Poncelet Porisms and Beyond

Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics

Birkhäuser
  • Self-contained, with an elementary introduction
  • Contains a complete account of higher-dimensional generalizations of Poncelet theorem, the corresponding Cayley-type conditions, and the Poncelet-Darboux grids.
  • Gives introspection into exciting interlacing of different areas of mathematics around the Poncelet porism.
  • Contains most modern results connected with the problems of Poncelet type.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Frontiers in Mathematics (FM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-vii
  2. Introduction to Poncelet Porisms

    • Vladimir Dragović, Milena Radnović
    Pages 1-9
  3. Billiards – First Examples

    • Vladimir Dragović, Milena Radnović
    Pages 11-25
  4. Hyperelliptic Curves and Their Jacobians

    • Vladimir Dragović, Milena Radnović
    Pages 27-66
  5. Projective Geometry

    • Vladimir Dragović, Milena Radnović
    Pages 67-105
  6. Poncelet Theorem and Cayley’s Condition

    • Vladimir Dragović, Milena Radnović
    Pages 107-135
  7. Poncelet–Darboux Curves and Siebeck–Marden Theorem

    • Vladimir Dragović, Milena Radnović
    Pages 137-164
  8. Ellipsoidal Billiards and Their Periodical Trajectories

    • Vladimir Dragović, Milena Radnović
    Pages 165-202
  9. Billiard Law and Hyperelliptic Curves

    • Vladimir Dragović, Milena Radnović
    Pages 203-225
  10. Poncelet Theorem and Continued Fractions

    • Vladimir Dragović, Milena Radnović
    Pages 227-257
  11. Quantum Yang–Baxter Equation and (2-2)-correspondences

    • Vladimir Dragović, Milena Radnović
    Pages 259-277
  12. Back Matter

    Pages 279-293

About this book

The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.

Reviews

From the reviews:

“The book provides a self-guided introduction to a set of classical gems that have to do with elliptic or hyperelliptic addition theorems; several connections were worked out originally by the authors in previous research papers. In addition, solutions to some of the integrable systems that came of age in the 1970s … are produced in this context. The style is clear and the calculations are complete. … it is certainly a focused, enjoyable and valuable one.” (Emma Previato, Mathematical Reviews, Issue 2012 j)

“Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians, and Pencils of Quadrics … gives a nice picture of both Poncelet’s Porism and a number of the areas of mathematics that are close by. … Dragović and Radnović do a good job of covering a wide range of material, including both citations and descriptions of classical material as well as extremely cutting-edge results. … The exposition in the book is generally good, and … any mathematician who picks up this book will learn something from it.” (Darren Glass, The Mathematical Association of America, September, 2011)

Authors and Affiliations

  • , Mathematical Institute, SANU, Belgrade, Serbia

    Vladimir Dragović, Milena Radnović

Bibliographic Information

  • Book Title: Poncelet Porisms and Beyond

  • Book Subtitle: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics

  • Authors: Vladimir Dragović, Milena Radnović

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-0015-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel AG 2011

  • Softcover ISBN: 978-3-0348-0014-3Published: 06 May 2011

  • eBook ISBN: 978-3-0348-0015-0Published: 02 May 2011

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: VIII, 294

  • Number of Illustrations: 74 b/w illustrations, 1 illustrations in colour

  • Topics: Algebraic Geometry

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access