Poincaré and the Three Body Problem.

Cover -- Title page -- Dedication -- Contents -- Acknowledgements -- Photograph and figure credits -- Chapter 1. Introduction -- Chapter 2. Historical background -- Chapter 3. Poincare's work before 1889 -- Chapter 4. Oscar II's 60th birthday competition -- Chapter 5. Poincare's Memoirs on the three body problem -- Chapter 6. Reception of Poincare's memoir -- Chapter 7. Poincare's related work after 1889 -- Chapter 8. Associated mathematical activity -- Chapter 9. Hadamard and Birkoff -- Chapter 10. Epilogue -- Appendix 1. A letter from Gosta Mittag-Leffler to Sonya -- Appendix 2. Announcement of the Oscar competition -- Appendix 3. Entries recieved in the Oscar competition -- Appendix 4. Report of the Prize commission -- Appendix 5. Title pages and tables of contents -- Appendix 6. Theorems in [P1] not included in [P2] -- Index -- Back Cover.

The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem-to describe the paths of three bodies in mutual gravitational interaction-is one of those which is simple to pose but impossible to solve precisely. Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincaré's subsequent highly influential work in celestial mechanics.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.