# American Institute of Mathematical Sciences

August  2013, 6(4): 925-974. doi: 10.3934/dcdss.2013.6.925

## Dynamics of the the dihedral four-body problem

 1 Deptartment of Mathematics and Applications, University of Milano-Bicocca 2 Via R. Cozzi, 53, 20125 Milano 3 Dipartimento di Matematica e Fisica Ennio De Giorgi 4 Universit del Salento 5 73100 Lecce

Received  October 2011 Revised  April 2012 Published  December 2012

Consider four point particles with equal masses in the euclideanspace,subject to the following symmetry constraint: at each instant theyare symmetric with respect to the dihedral group $D_2$,that is the groupgenerated by two rotations of angle $\pi$ around twoorthogonal axes.Under ahomogeneous potential of degree $-\alpha$ for $0<\alpha<2$,this is a subproblem of the four-body problem,inwhich all orbits have zero angular momentum and the configurationspace is three-dimensional.In this paper westudy the flow in McGehee coordinates on the collision manifold,anddiscuss the qualitative behavior of orbits which reach or come close to a total collision.
Citation: Davide L. Ferrario, Alessandro Portaluri. Dynamics of the the dihedral four-body problem. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 925-974. doi: 10.3934/dcdss.2013.6.925
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