Multiple geometrically distinct closed

noncollision orbits of fixed energy

for N-body type problems

with strong force potentials

Author:
Zhang Shiqing

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3039-3046

MSC (1991):
Primary 34C25, 34C15, 58F05

DOI:
https://doi.org/10.1090/S0002-9939-96-03751-3

MathSciNet review:
1371142

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using the equivariant Ljusternik-Schnirelmann theory, we prove that there are at least geometrically distinct noncollision orbits with prescribed energy for a class of planar N-body type problems with strong force potentials.

**[1]**A. Ambrosetti and V. Coti Zelati,*Closed orbits of fixed energy for a class of N-body problems*, Ann. IHP Analyse Nonlineaire**9**(1992), 187--200. MR**93e:58156a****[2]**A. Bari and P. H. Rabinowitz,*Periodic solutions of Hamiltonian systems of -body type*, Ann. IHP Analyse Nonlineaire**8**(1991), 561--649. MR**92k:58223****[3]**U. Bessi and V. Coti Zelati,*Symmetries and non-collision closed orbits for planar N-body type problems*, J. Nonlinear Anal. T.M.A.**16**(1991), 587--598. MR**92a:70006****[4]**V. Coti Zelati,*A class of periodic solutions of the N-body problem*, Celestial Mech.**46**(1989), 177--186. MR**91c:58116****[5]**------,*The periodic solutions of N-body type problems*, Ann. IHP Analyse Nonlineaire**7**(1990), 477--492. MR**93a:70009****[6]**E. Fadell and S. Husseini,*Infinite cuplength in free loop spaces with an application to a problem of the N-body type*, Ann. IHP Analyse Nonlineaire**9**(1992), 305--319. MR**94a:58034****[7]**W. Gordon,*Conservative dynamical systems involving strong forces*, Trans. Amer. Math. Soc.**204**(1975), 113--135. MR**51:14152****[8]**E. W. C. Van Groesen,*Analytical min-max methods for Hamiltonian break orbits of prescribed energy*, J. Math. Anal. Appl.**132**(1988), 1--12. MR**89m:58062****[9]**P. Majer and S. Terracini,*Periodic solutions to some N-body type problems*, preprint, 1992.**[10]**P. Rabinowitz,*Minimax methods in critical point theory with applications to differential equations*, C.B.M.S. Reg. Conf. Ser. in Math.**65**(1986). MR**87j:58024****[11]**E. Serra and S. Terracini,*Noncollision solutions to some three-body problems*, Arch. Rational Mech. Anal.**120**(1992), 305--325. MR**93i:70013****[12]**------,*Noncollision solutions to some singular minimization problems with Keplerian-like potentials*, Nonlinear Analysis T.M.A.**22**(1994), 45--62. MR**94m:58091****[13]**C. L. Siegel and K. Moser,*Lectures on celestial mechanics*, Springer-Verlag, 1971. MR**58:19464****[14]**S. Q. Zhang,*Multiple closed orbits of fixed energy for N-body-type problems with gravitational potentials*, preprint.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
34C25,
34C15,
58F05

Retrieve articles in all journals with MSC (1991): 34C25, 34C15, 58F05

Additional Information

**Zhang Shiqing**

Affiliation:
Department of Applied Mathematics, Chongqing University, Chongqing 630044, People’s Republic of China

Email:
cul@cbistic.sti.ac.cn

DOI:
https://doi.org/10.1090/S0002-9939-96-03751-3

Keywords:
N-body type problems with fixed energy,
geometrically distinct noncollision periodic orbits,
equivariant Ljusternik-Schnirelmann theory

Received by editor(s):
January 11, 1995

Communicated by:
James Glimm

Article copyright:
© Copyright 1996
American Mathematical Society