Four Open Questions for the N-Body Problem

Examining the classical N-body problem, this book demonstrates that the field is still vibrant, exploring four of the big open questions. It describes the progress made, emphasizing open areas of research. For mathematicians, physicists, and astronomers curious about the N-body problem, this book presents the state of the art.

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.