Four Open Questions for the N-Body Problem (Hardcover) (ISBN-13: 9781009200585)

The N-body problem has been investigated since Isaac Newton, however vast tracts of the problem remain open. Showcasing the vibrancy of the problem, this book describes four open questions and explores progress made over the last 20 years. After a comprehensive introduction, each chapter focuses on a different open question, highlighting how the stance taken and tools used vary greatly depending on the question. Progress on question one, 'Are the central configurations finite?', uses tools from algebraic geometry. Two, 'Are there any stable periodic orbits?', is dynamical and requires some understanding of the KAM theorem. The third, 'Is every braid realised?', requires topology and variational methods. The final question, 'Does a scattered beam have a dense image?', is quite new and formulating it precisely takes some effort. An excellent resource for students and researchers of mathematics, astronomy, and physics interested in exploring state-of-the-art techniques and perspectives on this classical problem.

Author: Richard Montgomery
ISBN-10: 1009200585
ISBN-13: 9781009200585
Publisher: Cambridge University Press
Language: English
Published: 12/19/2024
Pages: 312
Format: Hardcover
Weight: 1.29lbs
Size: 9.00h x 6.00w x 0.75d