Four Open Questions for the N-Body Problem

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.

• Emphasizes the vitality of the field through open problems, summarizing the methods used and providing readers with ideas for new research directions
• Accessible to those working in any area of mathematics, with the necessary physics covered in an introductory chapter and dedicated appendix
• Takes an intrinsic geometric approach to formulating the problems, allowing readers to draw pictures of higher-dimensional problems and build intuition not available through standard treatments