{"product_id":"four-open-questions-for-the-n-body-problem-hardback-9781009200585","title":"Four Open Questions for the N-Body Problem (Hardback) 9781009200585","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFour Open Questions for the N-Body Problem\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eRe-examine the classical N-body problem and explore state-of-the-art research into four of its big open questions.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eRichard Montgomery (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009200585, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 19 December 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e312 pages\u003cbr\u003e23.6 x 16 x 2 cm, 0.588 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Tour, Problem, and Structures: -1. A tour of solutions\u003cbr\u003e 0. The problem and its structure\u003cbr\u003e Part II. The Questions: 1. Are the central configurations finite?\u003cbr\u003e 2. Are there any stable periodic orbits?\u003cbr\u003e 3. Is every braid realized?\u003cbr\u003e 4. Does a scattered beam have a dense image?\u003cbr\u003e Appendices: A. Geometric mechanics\u003cbr\u003e B. Reduction and Poisson brackets\u003cbr\u003e C. The three-body problem and the shape sphere\u003cbr\u003e D. The orthogonal group and its Lie algebra\u003cbr\u003e E. Braids, homotopy and homology\u003cbr\u003e F. The Jacobi–Maupertuis metric\u003cbr\u003e G. Regularizing binary collisions\u003cbr\u003e H. One-degree of freedom and central scattering\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52472080269592,"sku":"9781009200585","price":30.45,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009200585i.jpg?v=1785716448","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/four-open-questions-for-the-n-body-problem-hardback-9781009200585","provider":"Freshly Printed Books","version":"1.0","type":"link"}