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The Integral Manifolds of the Three Body Problem

By: Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang

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The Integral Manifolds of the Three Body Problem

By: Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang

The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. 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 Birkhoffs conjecture that the bifurcations occur only at central configurations.

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Page Count

106

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806920

ISBN 13

9780821806920

The Integral Manifolds of the Three Body Problem

By: Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang

Write a review Read reviews Take a Quiz Solve Book Puzzle

The Integral Manifolds of the Three Body Problem

By: Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang

The phase space of the spatial three-body problem is an open subset in R18. Holding the ten classical integrals of energu, center of mass, linear and angular momentum fixed defines an eight dimensional manifold. 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 Birkhoffs conjecture that the bifurcations occur only at central configurations.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

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Solve jigsaw puzzle

Age

Page Count

106

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806920

ISBN 13

9780821806920

Book's by Quidong Wang

The Integral Manifolds of the Three Body Problem

The Integral Manifolds of the Three Body Problem

The Integral Manifolds of the Three Body Problem

The Integral Manifolds of the Three Body Problem

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