The Integral Manifolds of the Three Body Problem (Memoirs of the American Mathematical Society)

The Integral Manifolds of the Three Body Problem (Memoirs of the American Mathematical Society)

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Description

The phase space of the spatial three-body 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 well-known 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.

Contents

Introduction The decomposition of the spaces The cohomology The analysis of ${\mathfrak K}(c,h)$for equal masses The analysis of ${\mathfrak K}(c,h)$ for general masses Bibliography.

Product Details

  • ISBN13: 9780821806920
  • Format: Paperback
  • Number Of Pages: 92
  • ID: 9780821806920
  • ISBN10: 0821806920

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