journal article Jan 01, 2020

Almost all 3-body relative equilibria on <inline-formula><tex-math id="M1">$ \mathbb S^2 $</tex-math></inline-formula> and <inline-formula><tex-math id="M2">$ \mathbb H^2 $</tex-math></inline-formula> are inclined

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References
27
[4]
<p>F. Diacu, Relative equilibria in the 3-dimensional curved $n$-body problem, <i>Mem. Amer. Math. Soc.</i>, <b>228</b> (2014), ⅵ+80 pp.</p>
[5]
<p>F. Diacu, Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem, <i>J. Math. Phys.</i>, <b>57</b> (2016), 112701, 20pp.</p> 10.1063/1.4967443
[10]
<p>F. Diacu and S. Popa, All the Lagrangian relative equilibria of the curved 3-body problem have equal masses, <i>J. Math. Phys.</i>, <b>55</b> (2014), 112701, 9pp.</p> 10.1063/1.4900833
[12]
<p>F. Diacu, C. Stoica and S. Zhu, Central configurations of the curved <i>N</i>-body problem, <i>J. Nonlinear Sci.</i>, <b>28</b> (2018), 1999–2046, arXiv: 1603.03342.</p> 10.1007/s00332-018-9473-y
[13]
<p>M. W. Hirsch, <i>Differential Topology</i>, Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York-Heidelberg, 1976.</p> 10.1007/978-1-4684-9449-5
[16]
<p>J. Llibre, R. Moeckel and C. Simó, <i>Central Configurations, Periodic Orbits, and Hamiltonian Systems</i>, Advanced Courses in Mathematics. CRM Barcelona, Lecture notes given at the Centre de Recerca Matemàtica (CRM), Barcelona, January 27–31, 2014, Edited by Montserrat Corbera, Josep Maria Cors and Enrique Ponce, Birkhäuser Springer, Basel, 2015.</p> 10.1007/978-3-0348-0933-7
[18]
[19]
[20]
<p>A. V. Shchepetilov, <i>Calculus and Mechanics on Two-Point Homogeneous Riemannian Spaces</i>, Lecture Notes in Physics, Springer, Berlin, 2006.</p>
[22]
<p>S. Smale, Problems on the nature of relative equilibria in celestial mechanics, in <i>Manifolds –Amsterdam 1970 (Proc. Nuffic Summer School)</i>, Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, (1971), 194–198.</p> 10.1007/bfb0068618
[23]
[25]
<p>S. Zhu and S. Zhao, Three-dimensional central configurations in <inline-formula><tex-math id="M320">$ {\Bbb {H}}^3 $</tex-math></inline-formula> and <inline-formula><tex-math id="M1321">$ {\Bbb {S}}^3 $</tex-math></inline-formula>, <i>J. Math. Phys.</i>, <b>58</b> (2017), 022901, 7pp.</p>
[26]
<p>S. Zhu, A lower bound for the number of central configurations on <inline-formula><tex-math id="M1322">$ {\mathbb {H}}^2 $</tex-math></inline-formula>, preprint, arXiv: 1702.05535.</p>
[27]
<p>S. Zhu, On Dziobek special central configurations, preprint, arXiv: 1705.03987.</p>
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Published
Jan 01, 2020
Vol/Issue
13(4)
Pages
1131-1143
Cite This Article
Florin Diacu, Shuqiang Zhu (2020). Almost all 3-body relative equilibria on &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;$ \mathbb S^2 $&lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;$ \mathbb H^2 $&lt;/tex-math&gt;&lt;/inline-formula&gt; are inclined. Discrete and Continuous Dynamical Systems - S, 13(4), 1131-1143. https://doi.org/10.3934/dcdss.2020067