eBook ISBN:  9781470402174 
Product Code:  MEMO/132/628.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 
eBook ISBN:  9781470402174 
Product Code:  MEMO/132/628.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $29.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 132; 1998; 91 ppMSC: Primary 70; 58; 57
The phase space of the spatial threebody problem is an open subset in \({\mathbb R}^{18}\). Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the wellknown bifurcations due to central configurations, and three are due to “critical points at infinity”. This disproves Birkhoff's conjecture that the bifurcations occur only at central configurations.
ReadershipGraduate students and research mathematicians and physicists working in celestial mechanics.

Table of Contents

Chapters

1. Introduction

2. The decomposition of the spaces

3. The cohomology

4. The analysis of $\mathfrak {K}(c, h)$ for equal masses

5. The analysis of $\mathfrak {K}(c, h)$ for general masses


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The phase space of the spatial threebody problem is an open subset in \({\mathbb R}^{18}\). Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the wellknown bifurcations due to central configurations, and three are due to “critical points at infinity”. This disproves Birkhoff's conjecture that the bifurcations occur only at central configurations.
Graduate students and research mathematicians and physicists working in celestial mechanics.

Chapters

1. Introduction

2. The decomposition of the spaces

3. The cohomology

4. The analysis of $\mathfrak {K}(c, h)$ for equal masses

5. The analysis of $\mathfrak {K}(c, h)$ for general masses