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Making the moon reverse its orbit, or, stuttering in the planar threebody problem
1.  Department of Mathematics, University of North Carolina Asheville, CPO#2350 Asheville, NC 288048511, United States 
2.  Department of Mathematics, Penn State, State College, PA 16801, United States 
3.  Mathematics Department, University of California, Santa Cruz, CA 95064, United States 
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Hiroshi Ozaki, Hiroshi Fukuda, Toshiaki Fujiwara. Determination of motion from orbit in the threebody problem. Conference Publications, 2011, 2011 (Special) : 11581166. doi: 10.3934/proc.2011.2011.1158 
[2] 
KuoChang Chen. On ChencinerMontgomery's orbit in the threebody problem. Discrete & Continuous Dynamical Systems  A, 2001, 7 (1) : 8590. doi: 10.3934/dcds.2001.7.85 
[3] 
Xiaojun Chang, Tiancheng Ouyang, Duokui Yan. Linear stability of the crisscross orbit in the equalmass threebody problem. Discrete & Continuous Dynamical Systems  A, 2016, 36 (11) : 59715991. doi: 10.3934/dcds.2016062 
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Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted threebody problem. Discrete & Continuous Dynamical Systems  A, 1995, 1 (4) : 463474. doi: 10.3934/dcds.1995.1.463 
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Edward Belbruno. Random walk in the threebody problem and applications. Discrete & Continuous Dynamical Systems  S, 2008, 1 (4) : 519540. doi: 10.3934/dcdss.2008.1.519 
[6] 
Richard Moeckel. A topological existence proof for the Schubart orbits in the collinear threebody problem. Discrete & Continuous Dynamical Systems  B, 2008, 10 (2&3, September) : 609620. doi: 10.3934/dcdsb.2008.10.609 
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Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 299312. doi: 10.3934/dcds.2011.30.299 
[8] 
Richard Moeckel. A proof of Saari's conjecture for the threebody problem in $\R^d$. Discrete & Continuous Dynamical Systems  S, 2008, 1 (4) : 631646. doi: 10.3934/dcdss.2008.1.631 
[9] 
Jungsoo Kang. Some remarks on symmetric periodic orbits in the restricted threebody problem. Discrete & Continuous Dynamical Systems  A, 2014, 34 (12) : 52295245. doi: 10.3934/dcds.2014.34.5229 
[10] 
Rongchang Liu, Jiangyuan Li, Duokui Yan. New periodic orbits in the planar equalmass threebody problem. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 21872206. doi: 10.3934/dcds.2018090 
[11] 
Regina Martínez, Carles Simó. On the stability of the Lagrangian homographic solutions in a curved threebody problem on $\mathbb{S}^2$. Discrete & Continuous Dynamical Systems  A, 2013, 33 (3) : 11571175. doi: 10.3934/dcds.2013.33.1157 
[12] 
Abimael Bengochea, Manuel Falconi, Ernesto PérezChavela. Horseshoe periodic orbits with one symmetry in the general planar threebody problem. Discrete & Continuous Dynamical Systems  A, 2013, 33 (3) : 9871008. doi: 10.3934/dcds.2013.33.987 
[13] 
Qinglong Zhou, Yongchao Zhang. Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic threebody problem. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 17631787. doi: 10.3934/dcds.2017074 
[14] 
Tiancheng Ouyang, Duokui Yan. Variational properties and linear stabilities of spatial isosceles orbits in the equalmass threebody problem. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 39894018. doi: 10.3934/dcds.2017169 
[15] 
Niraj Pathak, V. O. Thomas, Elbaz I. Abouelmagd. The perturbed photogravitational restricted threebody problem: Analysis of resonant periodic orbits. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 849875. doi: 10.3934/dcdss.2019057 
[16] 
Hadia H. Selim, Juan L. G. Guirao, Elbaz I. Abouelmagd. Libration points in the restricted threebody problem: Euler angles, existence and stability. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 703710. doi: 10.3934/dcdss.2019044 
[17] 
JeanBaptiste Caillau, Bilel Daoud, Joseph Gergaud. Discrete and differential homotopy in circular restricted threebody control. Conference Publications, 2011, 2011 (Special) : 229239. doi: 10.3934/proc.2011.2011.229 
[18] 
Frederic Gabern, Àngel Jorba, Philippe Robutel. On the accuracy of restricted threebody models for the Trojan motion. Discrete & Continuous Dynamical Systems  A, 2004, 11 (4) : 843854. doi: 10.3934/dcds.2004.11.843 
[19] 
Anete S. Cavalcanti. An existence proof of a symmetric periodic orbit in the octahedral sixbody problem. Discrete & Continuous Dynamical Systems  A, 2017, 37 (4) : 19031922. doi: 10.3934/dcds.2017080 
[20] 
Mark Lewis, Daniel Offin, PietroLuciano Buono, Mitchell Kovacic. Instability of the periodic hiphop orbit in the $2N$body problem with equal masses. Discrete & Continuous Dynamical Systems  A, 2013, 33 (3) : 11371155. doi: 10.3934/dcds.2013.33.1137 
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