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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  8. The Three Body Problem, Elsevier, Amsterdam, 1990. (1990) Zbl0719.70006MR1124619
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  11. Off to infinity in finite time, Notices Amer. Math. Soc. 42 (1995), 538–546. (1995) MR1324734

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