Library Of American University Of Madaba
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Dragović, Vladimir.
Poncelet Porisms and Beyond Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics / [electronic resource] : by Vladimir Dragović, Milena Radnović. - VIII, 294p. 75 illus., 1 illus. in color. online resource. - Frontiers in Mathematics, 1660-8046 .
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.
9783034800150
Mathematics.
Geometry, algebraic.
Mathematics.
Algebraic Geometry.
QA564-609
516.35
Poncelet Porisms and Beyond Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics / [electronic resource] : by Vladimir Dragović, Milena Radnović. - VIII, 294p. 75 illus., 1 illus. in color. online resource. - Frontiers in Mathematics, 1660-8046 .
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.
9783034800150
Mathematics.
Geometry, algebraic.
Mathematics.
Algebraic Geometry.
QA564-609
516.35