Papers on Fuchsian Functions

Henri Poincare

ISBN 10: 1461295823 / ISBN 13: 9781461295822

Editore: Springer New York, 2012

Riguardo questo articolo

reprint edition. 483 pages. 9.25x6.10x1.10 inches. In Stock.

Codice articolo x-1461295823

Dati bibliografici

• Titolo: Papers on Fuchsian Functions
• Editore: Springer New York
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461295823
• ISBN 13: 9781461295822
• Rilegatura: Paperback
• Condizione: Brand New

Descrizione articolo

Riassunto

by John Stillwell I. General Reaarb , Poincare's papers on Fuchsian and Kleinian I1'OUps are of Il'eat interest from at least two points of view: history, of course, but also as an inspiration for further mathematical proll'ess. The papers are historic as the climax of the ceometric theory of functions initiated by Riemann, and ideal representatives of the unity between analysis, ceometry, topololY and alcebra which prevailed during the 1880's. The rapid mathematical prOll'ess of the 20th century has been made at the expense of unity and historical perspective, and if mathematics is not to disintell'ate altogether, an effort must sometime be made to find its , main threads and weave them tocether 81ain. Poincare's work is an excellent example of this process, and may yet prove to be at the core of a . new synthesis. Certainly, we are now able to gather up , some of the loose ends in Poincare, and a broader synthesis seems to be actually taking place in the work of Thurston. The papers I have selected include the three Il'eat memoirs in the first volumes of Acta Math. -tice, on· Fuchsian groups, Fuchsian , functions, and Kleinian groups (Poincare [1882 a,b,1883]). These are the papers which made his reputation and they include many results and proofs which are now standard. They are preceded by an , unedited memoir written by Poincare in May 1880 at the height of his , creative ferment.

Contenuti

Translator’s Introduction.- Annotated Table of Contents.- On Fuchsian Functions.- On Fuchsian Functions.- Theory of Fuchsian Groups.- On Fuchsian Functions.- Memoir on Kleinian Groups.- Extract from an unedited memoir of Henri Poincaré on Fuchsian functions.- On the Groups of Linear Equations.