An alternative proof of Painlevé's theorem

Jan Němec

Applications of Mathematics (2000)

  • Volume: 45, Issue: 4, page 291-299
  • ISSN: 0862-7940

Abstract

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In this article we show some aspects of analytical and numerical solution of the n -body problem, which arises from the classical Newtonian model for gravitation attraction. We prove the non-existence of stationary solutions and give an alternative proof for Painlevé’s theorem.

How to cite

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Němec, Jan. "An alternative proof of Painlevé's theorem." Applications of Mathematics 45.4 (2000): 291-299. <http://eudml.org/doc/33060>.

@article{Němec2000,
abstract = {In this article we show some aspects of analytical and numerical solution of the $n$-body problem, which arises from the classical Newtonian model for gravitation attraction. We prove the non-existence of stationary solutions and give an alternative proof for Painlevé’s theorem.},
author = {Němec, Jan},
journal = {Applications of Mathematics},
keywords = {$n$-body problem; ordinary differential equations; Painlevé’s theorem; -body problem; ordinary differential equations; Painlevé theorem},
language = {eng},
number = {4},
pages = {291-299},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An alternative proof of Painlevé's theorem},
url = {http://eudml.org/doc/33060},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Němec, Jan
TI - An alternative proof of Painlevé's theorem
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 4
SP - 291
EP - 299
AB - In this article we show some aspects of analytical and numerical solution of the $n$-body problem, which arises from the classical Newtonian model for gravitation attraction. We prove the non-existence of stationary solutions and give an alternative proof for Painlevé’s theorem.
LA - eng
KW - $n$-body problem; ordinary differential equations; Painlevé’s theorem; -body problem; ordinary differential equations; Painlevé theorem
UR - http://eudml.org/doc/33060
ER -

References

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  1. Foundation of Celestial Mechanics, Academia, Praha, 1971. (Czech) (1971) 
  2. Celestial Mechanics, Academia, Praha, 1987. (Czech) (1987) 
  3. Ordinary Differential Equations in Real Space, Univerzita Karlova, Praha, 1990. (Czech) (1990) 
  4. On the three-body problem, Rozhledy mat.-fyz. 70 (1992), 105–112. (Czech) (1992) 
  5. 10.1016/0377-0427(95)00067-4, Comput. Appl. Math. 63 (1995), 403–409. (1995) MR1365579DOI10.1016/0377-0427(95)00067-4
  6. 10.1016/S0378-4754(99)00085-3, Math. Comput. Simulation 50 (1999), 237–245. (1999) MR1717610DOI10.1016/S0378-4754(99)00085-3
  7. Ordinary Differential Equations, Elsevier, Amsterdam, 1986. (1986) Zbl0667.34002MR0929466
  8. The Three Body Problem, Elsevier, Amsterdam, 1990. (1990) Zbl0719.70006MR1124619
  9. Numerical Solution of the N -Body Problem, Reidel Publishing Company, Dordrecht, 1985. (1985) MR0808778
  10. Leçons sur la Théorie Analytic des Equations Différentielles, Hermann, Paris, 1897. (1897) 
  11. Off to infinity in finite time, Notices Amer. Math. Soc. 42 (1995), 538–546. (1995) MR1324734

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