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A topological existence proof for the Schubart orbits in the collinear threebody problem
1.  School of Mathematics, University of Minnesota, Minneapolis MN 55455, United States 
[1] 
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 
[2] 
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 
[3] 
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 
[4] 
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 
[5] 
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 
[6] 
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 
[7] 
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 
[8] 
Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 299312. doi: 10.3934/dcds.2011.30.299 
[9] 
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 
[10] 
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 
[11] 
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 
[12] 
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 
[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] 
Samuel R. Kaplan, Mark Levi, Richard Montgomery. Making the moon reverse its orbit, or, stuttering in the planar threebody problem. Discrete & Continuous Dynamical Systems  B, 2008, 10 (2&3, September) : 569595. doi: 10.3934/dcdsb.2008.10.569 
[15] 
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 
[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] 
NaiChia Chen. Symmetric periodic orbits in three subproblems of the $N$body problem. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 15231548. doi: 10.3934/dcdsb.2014.19.1523 
[18] 
Daniel Offin, Hildeberto Cabral. Hyperbolicity for symmetric periodic orbits in the isosceles three body problem. Discrete & Continuous Dynamical Systems  S, 2009, 2 (2) : 379392. doi: 10.3934/dcdss.2009.2.379 
[19] 
Alessandra Celletti. Some KAM applications to Celestial Mechanics. Discrete & Continuous Dynamical Systems  S, 2010, 3 (4) : 533544. doi: 10.3934/dcdss.2010.3.533 
[20] 
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 
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