When the novel begins in the 1960s, China is in the midst of its Cultural Revolution in which various factions in the Communist Party – especially among younger members – accuse one another of not being radical enough. “The Three-Body Problem” is a science fiction novel by Cixin Liu (and translated by Ken Liu) which traces the efforts of disillusioned Chinese scientists who implore alien life to come to Earth to forcibly redeem humanity. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions.NOTE: This study guide refers to the 2014 Tor Paperback edition and translation by Ken Liu of "The Three-Body Problem" by Cixin Liu. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincare's subsequent highly influential work in celestial mechanics. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition.
Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work. In correcting this error Poincare discovered mathematical chaos, as is now clear from June Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm.
His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. Poincare's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway.