Poincaré and the Three Body Problem

Barrow-Green, June Elizabeth (1993). Poincaré and the Three Body Problem. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000e03b


The purpose of the thesis is to present an account of Henri Poincare's famous memoir on the three body problem, the final version of which was published in Acta Mathematica in 1890 as the prize-winning entry in King Oscar II's 60th birthday competition. The memoir is reknowned both for its role in providing the foundations for Poincare's celebrated three volume Méthodes Nouvelles de la Mécanique Céleste, and for containing the first mathematical description of chaotic behaviour in a dynamical system.

A historical context is provided both through consideration of the problem itself and through a discussion of Poincaré's earlier work which relates to the mathematics developed in the memoir. The organisation of the Oscar competition, which was undertaken by Gösta Mittag-Leffler, is also described. This not only provides an insight into the late 19th century European mathematical community but also reveals that after the prize had been awarded Poincare found an important error in his work and substantially revised the memoir prior to its publication in Acta. The discovery of a printed version of the original memoir personally annotated by Poincaré has allowed for a detailed comparative study of the mathematics contained in both versions of the memoir. The error is explained and it is shown that it was only as a result of its correction that Poincaré discovered the chaotic behaviour now associated with the memoir.

The contemporary reception of the memoir is discussed and Poincaré's subsequent work in celestial mechanics and related topics is examined. Through the consideration of sources up to 1920 the influence and impact of the memoir on the progress of the three body problem and on dynamics in general is assessed.

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