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Random walk in the three-body problem and applications
Symbolic dynamics of the elliptic rectilinear restricted 3--body problem
1. | Department of Mathematics, University of North Carolina Asheville, CPO#2350 Asheville, NC 28804-8511, United States |
2. | Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, C.P. 09340 México, D.F., Mexico |
3. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona |
[1] |
Gianni Arioli. Branches of periodic orbits for the planar restricted 3-body problem. Discrete and Continuous Dynamical Systems, 2004, 11 (4) : 745-755. doi: 10.3934/dcds.2004.11.745 |
[2] |
Giovanni F. Gronchi, Chiara Tardioli. The evolution of the orbit distance in the double averaged restricted 3-body problem with crossing singularities. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1323-1344. doi: 10.3934/dcdsb.2013.18.1323 |
[3] |
Alain Albouy, Holger R. Dullin. Relative equilibria of the 3-body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020, 12 (3) : 323-341. doi: 10.3934/jgm.2020012 |
[4] |
Elbaz I. Abouelmagd, Juan Luis García Guirao, Jaume Llibre. Periodic orbits for the perturbed planar circular restricted 3–body problem. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1007-1020. doi: 10.3934/dcdsb.2019003 |
[5] |
Qunyao Yin, Shiqing Zhang. New periodic solutions for the circular restricted 3-body and 4-body problems. Communications on Pure and Applied Analysis, 2010, 9 (1) : 249-260. doi: 10.3934/cpaa.2010.9.249 |
[6] |
Holger R. Dullin, Jürgen Scheurle. Symmetry reduction of the 3-body problem in $ \mathbb{R}^4 $. Journal of Geometric Mechanics, 2020, 12 (3) : 377-394. doi: 10.3934/jgm.2020011 |
[7] |
Alain Chenciner, Jacques Féjoz. The flow of the equal-mass spatial 3-body problem in the neighborhood of the equilateral relative equilibrium. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 421-438. doi: 10.3934/dcdsb.2008.10.421 |
[8] |
Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
[9] |
Richard Moeckel. A topological existence proof for the Schubart orbits in the collinear three-body problem. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 609-620. doi: 10.3934/dcdsb.2008.10.609 |
[10] |
Eduardo Piña. Computing collinear 4-Body Problem central configurations with given masses. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1215-1230. doi: 10.3934/dcds.2013.33.1215 |
[11] |
Mitsuru Shibayama. Non-integrability of the collinear three-body problem. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 299-312. doi: 10.3934/dcds.2011.30.299 |
[12] |
Marcel Guardia, Tere M. Seara, Pau Martín, Lara Sabbagh. Oscillatory orbits in the restricted elliptic planar three body problem. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 229-256. doi: 10.3934/dcds.2017009 |
[13] |
Jungsoo Kang. Some remarks on symmetric periodic orbits in the restricted three-body problem. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5229-5245. doi: 10.3934/dcds.2014.34.5229 |
[14] |
Eduardo S. G. Leandro. On the Dziobek configurations of the restricted $(N+1)$-body problem with equal masses. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 589-595. doi: 10.3934/dcdss.2008.1.589 |
[15] |
Hsin-Yuan Huang. Schubart-like orbits in the Newtonian collinear four-body problem: A variational proof. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1763-1774. doi: 10.3934/dcds.2012.32.1763 |
[16] |
Tiancheng Ouyang, Zhifu Xie. Regularization of simultaneous binary collisions and solutions with singularity in the collinear four-body problem. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 909-932. doi: 10.3934/dcds.2009.24.909 |
[17] |
Nicola Soave, Susanna Terracini. Symbolic dynamics for the $N$-centre problem at negative energies. Discrete and Continuous Dynamical Systems, 2012, 32 (9) : 3245-3301. doi: 10.3934/dcds.2012.32.3245 |
[18] |
Davide L. Ferrario, Alessandro Portaluri. Dynamics of the the dihedral four-body problem. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 925-974. doi: 10.3934/dcdss.2013.6.925 |
[19] |
Niraj Pathak, V. O. Thomas, Elbaz I. Abouelmagd. The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 849-875. doi: 10.3934/dcdss.2019057 |
[20] |
Hadia H. Selim, Juan L. G. Guirao, Elbaz I. Abouelmagd. Libration points in the restricted three-body problem: Euler angles, existence and stability. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 703-710. doi: 10.3934/dcdss.2019044 |
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