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Infinity manifolds on energy levels for celestial mechanics

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Nonlinear Phenomena

Part of the book series: Lecture Notes in Physics ((LNP,volume 189))

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Abstract

We consider the n-body problem of celestial mechanics. Our goal will be to describe its energy surfaces with some added asymptotic boundaries, as well as to picture the kind of orbits arising in some simple examples. Among the asymptotic boundaries, we will mainly focus on the infinity manifolds [5], which describe escape orbits.

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References

  1. F. Calogero, Integrable dinamical systems and related mathematical results. These Proceedings.

    Google Scholar 

  2. R. Devaney, Singularities in classical mechanical systems. In Ergodic Theory and Dynamical Systems. Vol. I. (A. Katok, ed.) pp. 211–333, Birkhauser, Basel, 1981.

    Google Scholar 

  3. W. Kaplan,Topology of the two-body problem. Amer. Math. Monthly 49, 316–323 (1942).

    Google Scholar 

  4. E. Lacomba, Variétés de l'infini por une énergie non nulle en mécanique célèste. C.R.A.S., Paris 1295, 503–506 (1982).

    Google Scholar 

  5. E. Lacomba and C. Simó, Boundary manifolds for energy surfaces in celestial mechanics. Celestial Mechanics 28, 37–48 (1982).

    Article  Google Scholar 

  6. R. Mc Gehee, Triple collision in the collinear three-body problem. Inv. Math. 27, 191–227 (1974).

    Article  Google Scholar 

  7. R. Moeckel, Orbits of the three-body problem which pass infinitely close to triple collision. Amer. J. Math. 103, 1323–1341 (1981).

    Google Scholar 

  8. D. Saari, Singularities and collisions of Newtonian graviational systems. Arch. Rational Mech. Anal. 49, 311–320 (1973).

    Article  Google Scholar 

  9. H. Sperling, On the real singularities of the n-body problem. J. Reine Angew. Math. 145, 14–50 (1970).

    Google Scholar 

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K. B. Wolf

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© 1983 Springer-Verlag

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Lacomba, E.A. (1983). Infinity manifolds on energy levels for celestial mechanics. In: Wolf, K.B. (eds) Nonlinear Phenomena. Lecture Notes in Physics, vol 189. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12730-5_22

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  • DOI: https://doi.org/10.1007/3-540-12730-5_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12730-7

  • Online ISBN: 978-3-540-38721-3

  • eBook Packages: Springer Book Archive

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