caa a22 4500 445863013 CHVBK 20180317145449.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10569-010-9325-z doi (NATIONALLICENCE)springer-10.1007/s10569-010-9325-z Periodic solutions with alternating singularities in the collinear four-body problem [Elektronische Daten] [Tiancheng Ouyang, Duokui Yan] This paper gives an analytic proof of the existence of Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the Schubart-like orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proved by using a "turning point” technique and a continuity argument on differential equations of the regularized Hamiltonian. Springer Science+Business Media B.V., 2010 Celestial mechanics nationallicence Four-body problem nationallicence Binary collision nationallicence Simultaneous binary collision nationallicence Periodic solution with singularity nationallicence Ouyang Tiancheng Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut Yan Duokui Chern Institute of Mathematics, Nankai University, 300071, Tianjin, People's Republic of China aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/3(2011-03-01), 229-239 0923-2958 109:3<229 2011 109 10569 https://doi.org/10.1007/s10569-010-9325-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-010-9325-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ouyang Tiancheng Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut NATIONALLICENCE 700 1- Yan Duokui Chern Institute of Mathematics, Nankai University, 300071, Tianjin, People's Republic of China aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 109/3(2011-03-01), 229-239 0923-2958 109:3<229 2011 109 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer