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Second order oscillation of mixed nonlinear dynamic equations with several positive and negative coefficients
Determination of motion from orbit in the threebody problem
1.  General Education Program Center, Tokai University, 317 Nishino, Numazu, Shizuoka 4100395, Japan 
2.  College of Liberal Arts and Sciences, Kitasato University, 1151 Kitasato, Minamiku, Sagamihara, Kanagawa 2520373, Japan, Japan 
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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 
[2] 
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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Mitsuru Shibayama. Nonintegrability of the collinear threebody problem. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 299312. doi: 10.3934/dcds.2011.30.299 
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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 
[5] 
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 
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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 
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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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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 
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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 
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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 
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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 
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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] 
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 
[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] 
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 
[16] 
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 
[17] 
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 
[18] 
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 
[19] 
Marcel Guardia, Tere M. Seara, Pau Martín, Lara Sabbagh. Oscillatory orbits in the restricted elliptic planar three body problem. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 229256. doi: 10.3934/dcds.2017009 
[20] 
Florian Rupp, Jürgen Scheurle. Classification of a class of relative equilibria in three body coulomb systems. Conference Publications, 2011, 2011 (Special) : 12541262. doi: 10.3934/proc.2011.2011.1254 
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