Four Open Questions for the N-Body Problem
Cambridge University Press (Verlag)
978-1-009-20058-5 (ISBN)
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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.
Richard Montgomery is Professor Emeritus of Mathematics at University of California, Santa Cruz. He is a co-rediscoverer of the surprisingly stable figure eight orbit for the classical three-body problem. His work on the N-body problem uses variational, topological, and differential geometric methods to say new things about this old problem.
Part I. Tour, Problem, and Structures: -1. A tour of solutions; 0. The problem and its structure; Part II. The Questions: 1. Are the central configurations finite?; 2. Are there any stable periodic orbits?; 3. Is every braid realized?; 4. Does a scattered beam have a dense image?; Appendices: A. Geometric mechanics; B. Reduction and Poisson brackets; C. The three-body problem and the shape sphere; D. The orthogonal group and its Lie algebra; E. Braids, homotopy and homology; F. The Jacobi–Maupertuis metric; G. Regularizing binary collisions; H. One-degree of freedom and central scattering; References; Index.
| Erscheint lt. Verlag | 31.10.2024 |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik | |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| ISBN-10 | 1-009-20058-5 / 1009200585 |
| ISBN-13 | 978-1-009-20058-5 / 9781009200585 |
| Zustand | Neuware |
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