- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 173639, 8 pages
Periodic Solutions for Circular Restricted -Body Problems
1College of Mathematics, Sichuan University, Chengdu 610064, China
2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China
Received 18 February 2013; Accepted 3 April 2013
Academic Editor: Baodong Zheng
Copyright © 2013 Xiaoxiao Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Chenciner and R. Montgomery, “A remarkable periodic solution of the three-body problem in the case of equal masses,” Annals of Mathematics, vol. 152, no. 3, pp. 881–901, 2000.
- A. Chenciner, “Action minimizing solutions of the Newtonian n-body problem: from homology to symmetry,” in Proceedings of the International Mathematical Union (ICM '02), pp. 255–264, Beijing, China, 2002.
- A. Venturelli, “Une caractérisation variationnelle des solutions de Lagrange du problème plan des trois corps,” Comptes Rendus de l'Académie des Sciences, vol. 332, no. 7, pp. 641–644, 2001.
- C. Marchal, “How the method of minimization of action avoids singularities,” Celestial Mechanics & Dynamical Astronomy, vol. 83, no. 1–4, pp. 325–353, 2002.
- C. Moore, “Braids in classical dynamics,” Physical Review Letters, vol. 70, no. 24, pp. 3675–3679, 1993.
- C. Simó, “New families of solutions in -body problems,” Progress in Mathematics, vol. 201, pp. 101–115, 2001.
- D. L. Ferrario and S. Terracini, “On the existence of collisionless equivariant minimizers for the classical -body problem,” Inventiones Mathematicae, vol. 155, no. 2, pp. 305–362, 2004.
- F. Y. Li, S. Q. Zhang, and X. X. Zhao, “Periodic solutions for spatial restricted N+1-body problems,” Preprint.
- S. Zhang and Q. Zhou, “Symmetric periodic noncollision solutions for -body-type problems,” Acta Mathematica Sinica, vol. 11, no. 1, pp. 37–43, 1995.
- S. Q. Zhang and Q. Zhou, “A minimizing property of Lagrangian solutions,” Acta Mathematica Sinica, vol. 17, no. 3, pp. 497–500, 2001.
- S. Zhang and Q. Zhou, “Variational methods for the choreography solution to the three-body problem,” Science in China A, vol. 45, no. 5, pp. 594–597, 2002.
- S. Zhang and Q. Zhou, “Nonplanar and noncollision periodic solutions for -body problems,” Discrete and Continuous Dynamical Systema A, vol. 10, no. 3, pp. 679–685, 2004.
- S. Zhang, Q. Zhou, and Y. Liu, “New periodic solutions for 3-body problems,” Celestial Mechanics & Dynamical Astronomy, vol. 88, no. 4, pp. 365–378, 2004.
- U. Bessi and V. Coti Zelati, “Symmetries and noncollision closed orbits for planar -body-type problems,” Nonlinear Analysis, vol. 16, no. 6, pp. 587–598, 1991.
- X. X. Zhao and S. Q. Zhang, “Periodic solutions for circular restricted 4-body problems with Newtonian potentials,” Preprint.
- J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74, Springer, New York, NY, USA, 1989.
- M. Struwe, Variational Methods, Springer, Berlin, Germany, 3rd edition, 1990.
- R. S. Palais, “The principle of symmetric criticality,” Communications in Mathematical Physics, vol. 69, no. 1, pp. 19–30, 1979.
- W. B. Gordon, “A minimizing property of Keplerian orbits,” The American Journal of Mathematics, vol. 99, no. 5, pp. 961–971, 1977.
- Y. Long and S. Zhang, “Geometric characterizations for variational minimization solutions of the 3-body problem,” Acta Mathematica Sinica, vol. 16, no. 4, pp. 579–592, 2000.