Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Bifurcations of the Hill's Region in the Three Body Problem

Christopher K. McCord
Proceedings of the American Mathematical Society
Vol. 127, No. 7 (Jul., 1999), pp. 2135-2142
Stable URL: http://www.jstor.org/stable/119453
Page Count: 8
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Bifurcations of the Hill's Region in the Three Body Problem
Preview not available

Abstract

In the spatial three body problem, the topology of the integral manifolds M(c, h) (i.e. the level sets of energy h and angular momentum c, as well as center of mass and linear momentum) and the Hill's regions H(c, h) (the projection of the integral manifold onto position coordinates) depends only on the quantity ν = h|c|2. It was established by Albouy and McCord-Meyer-Wang that, for h < 0 and c ≠ 0, there are exactly eight bifurcation values for ν 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 ν 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.

Page Thumbnails

  • Thumbnail: Page 
2135
    2135
  • Thumbnail: Page 
2136
    2136
  • Thumbnail: Page 
2137
    2137
  • Thumbnail: Page 
2138
    2138
  • Thumbnail: Page 
2139
    2139
  • Thumbnail: Page 
2140
    2140
  • Thumbnail: Page 
2141
    2141
  • Thumbnail: Page 
2142
    2142