Abstract
Here we make a topological study of the mapI=(E, J), whereE is the energy andJ is the angular momentum of then-body problem in 3-space. Part of the bifurcation set ofI is characterized and some topological information is given on the integral manifolds of negative energy and zero angular momentum.
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References
Birkhoff, G. D.: Dynamical Systems. Rev. Ed. Colloq. Publ.9, Amer. Math. Soc., Providence, R. I., 1966.
Easton, R.: Some Topology of the 3-Body Problem. Journal of Differential Equations10, 371–377 (1971).
Lang, S.: Introduction to Differentiable Manifolds. New York: Wiley (Interscience) 1962.
Robbin, J. W.: Relative Equilibria in Mechanical Systems. Preprint. Univ. of Wisconsin, Madison, Wis.
Smale, S.: Topology and Mechanics. I. Inventiones math.10, 305–331 (1970).
Smale, S.: Topology and Mechanics, II. Inventiones math.11, 45–64 (1970).
Spanier, E. H.: Algebraic Topology. New York: McGraw-Hill 1966.
Wintner, A.: The Analytical Foundations of Celestial Mechanics. Princeton, N. J.: Princeton Univ. Press 1941.
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This paper is the author's doctoral dissertation prepared under the supervision of Professor S. Smale at the University of California, Berkeley. Part of this work was done during a 3 months visit at the Institut des Hautes Etudes Scientifiques.
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Cabral, H.E. On the integral manifolds of theN-body problem. Invent Math 20, 59–72 (1973). https://doi.org/10.1007/BF01405264
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DOI: https://doi.org/10.1007/BF01405264