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Regularization of simultaneous binary collisions and solutions with singularity in the collinear fourbody problem
1.  Department of Mathematics, Brigham Young University, Provo, Utah 84602, United States 
2.  Department of Mathematics and Computer Science, Virginia State University, Petersburg, Virginia 23806, United States 
[1] 
HsinYuan Huang. Schubartlike orbits in the Newtonian collinear fourbody problem: A variational proof. Discrete & Continuous Dynamical Systems  A, 2012, 32 (5) : 17631774. doi: 10.3934/dcds.2012.32.1763 
[2] 
Davide L. Ferrario, Alessandro Portaluri. Dynamics of the the dihedral fourbody problem. Discrete & Continuous Dynamical Systems  S, 2013, 6 (4) : 925974. doi: 10.3934/dcdss.2013.6.925 
[3] 
Duokui Yan, Tiancheng Ouyang, Zhifu Xie. Classification of periodic orbits in the planar equalmass fourbody problem. Conference Publications, 2015, 2015 (special) : 11151124. doi: 10.3934/proc.2015.1115 
[4] 
Chjan C. Lim, Joseph Nebus, Syed M. Assad. MonteCarlo and polyhedronbased simulations I: extremal states of the logarithmic Nbody problem on a sphere. Discrete & Continuous Dynamical Systems  B, 2003, 3 (3) : 313342. doi: 10.3934/dcdsb.2003.3.313 
[5] 
Ernesto A. Lacomba, Mario Medina. Oscillatory motions in the rectangular four body problem. Discrete & Continuous Dynamical Systems  S, 2008, 1 (4) : 557587. doi: 10.3934/dcdss.2008.1.557 
[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 
[7] 
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] 
Eduardo Piña. Computing collinear 4Body Problem central configurations with given masses. Discrete & Continuous Dynamical Systems  A, 2013, 33 (3) : 12151230. doi: 10.3934/dcds.2013.33.1215 
[9] 
Roberto Castelli, Susanna Terracini. On the regularization of the collision solutions of the onecenter problem with weak forces. Discrete & Continuous Dynamical Systems  A, 2011, 31 (4) : 11971218. doi: 10.3934/dcds.2011.31.1197 
[10] 
G. Bellettini, G. Fusco, G. F. Gronchi. Regularization of the twobody problem via smoothing the potential. Communications on Pure & Applied Analysis, 2003, 2 (3) : 323353. doi: 10.3934/cpaa.2003.2.323 
[11] 
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 
[12] 
Eduardo S. G. Leandro. On the Dziobek configurations of the restricted $(N+1)$body problem with equal masses. Discrete & Continuous Dynamical Systems  S, 2008, 1 (4) : 589595. doi: 10.3934/dcdss.2008.1.589 
[13] 
Marshall Hampton, Anders Nedergaard Jensen. Finiteness of relative equilibria in the planar generalized $N$body problem with fixed subconfigurations. Journal of Geometric Mechanics, 2015, 7 (1) : 3542. doi: 10.3934/jgm.2015.7.35 
[14] 
Frederic Gabern, Àngel Jorba. A restricted fourbody model for the dynamics near the Lagrangian points of the SunJupiter system. Discrete & Continuous Dynamical Systems  B, 2001, 1 (2) : 143182. doi: 10.3934/dcdsb.2001.1.143 
[15] 
Montserrat Corbera, Jaume Llibre. On the existence of bipyramidal central configurations of the $n+2$body problem with an $n$gon base. Discrete & Continuous Dynamical Systems  A, 2013, 33 (3) : 10491060. doi: 10.3934/dcds.2013.33.1049 
[16] 
YongKum Cho. A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem. Kinetic & Related Models, 2012, 5 (3) : 441458. doi: 10.3934/krm.2012.5.441 
[17] 
Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 5575. doi: 10.3934/era.2015.22.55 
[18] 
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 
[19] 
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 
[20] 
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 
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