Poncelet Porisms and Beyond [recurso electrónico] : Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics / by Vladimir Dragovic, Milena Radnovic.

Por: Dragovic, Vladimir [author.]Colaborador(es): Radnovic, Milena [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Frontiers in MathematicsEditor: Basel : Springer Basel, 2011Descripción: VIII, 294p. 75 illus., 1 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783034800150Tema(s): Mathematics | Geometry, algebraic | Mathematics | Algebraic GeometryFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 516.35 Clasificación LoC:QA564-609Recursos en línea: Libro electrónicoTexto
Contenidos:
Introduction to Poncelet Porisms -- Billiards – First Examples -- Hyper-Elliptic Curves and Their Jacobians -- Projective geometry -- Poncelet Theorem and Cayley’s Condition -- Poncelet–Darboux Curves and Siebeck–Marden Theorem -- Ellipsoidal Billiards and their Periodical Trajectories -- Billiard Law and Hyper-Elliptic Curves -- Poncelet Theorem and Continued Fractions -- Quantum Yang-Baxter equation and (2-2)-correspondences -- Bibliography -- Index.
En: Springer eBooksResumen: 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.
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Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA564 -609 (Browse shelf(Abre debajo)) 1 No para préstamo 373040-2001

Introduction to Poncelet Porisms -- Billiards – First Examples -- Hyper-Elliptic Curves and Their Jacobians -- Projective geometry -- Poncelet Theorem and Cayley’s Condition -- Poncelet–Darboux Curves and Siebeck–Marden Theorem -- Ellipsoidal Billiards and their Periodical Trajectories -- Billiard Law and Hyper-Elliptic Curves -- Poncelet Theorem and Continued Fractions -- Quantum Yang-Baxter equation and (2-2)-correspondences -- Bibliography -- Index.

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.

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