Bifurcations of the Hill's region

in the three body problem

Author:
Christopher K. McCord

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2135-2142

MSC (1991):
Primary 70F07; Secondary 57Q60, 58F14

DOI:
https://doi.org/10.1090/S0002-9939-99-04755-3

Published electronically:
March 3, 1999

MathSciNet review:
1487328

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Abstract | References | Similar Articles | Additional Information

Abstract: In the spatial three body problem, the topology of the integral manifolds (i.e. the level sets of energy and angular momentum , as well as center of mass and linear momentum) and the Hill's regions (the projection of the integral manifold onto position coordinates) depends only on the quantity It was established by Albouy and McCord-Meyer-Wang that, for and , there are exactly eight bifurcation values for at which the topology of the integral manifold changes. It was also shown that for each of these values, the topology of the Hill's region changes as well. In this work, it is shown that there are no other values of for which the topology of the Hill's region changes. That is, a bifurcation of the Hill's region occurs if and only if a bifurcation of the integral manifold occurs.

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Additional Information

**Christopher K. McCord**

Affiliation:
Institute for Dynamics, Department of Mathematics, University of Cincinnati, Cincinnati, Ohio 45221-0025

Email:
chris.mccord@uc.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04755-3

Received by editor(s):
June 11, 1997

Received by editor(s) in revised form:
October 14, 1997

Published electronically:
March 3, 1999

Additional Notes:
The author was supported in part by grants from the National Science Foundation and the Charles Phelps Taft Memorial Fund.

Communicated by:
Mary Rees

Article copyright:
© Copyright 1999
American Mathematical Society