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Additional resources for 16-dimensional compact projective planes with a collineation group of dimension >= 35
Differential Integral Equations, 5(1):103–136, 1992. 43  F. Diacu. Painlev´e’s conjecture. Math. Intelligencer, 15(2):6–12, 1993.  F. Diacu. Near-collision dynamics for particle systems with quasihomogeneous potentials. J. Differential Equations, 128(1):58–77, 1996.  F. Diacu. Singularities of the N -body problem. In Classical and celestial mechanics (Recife, 1993/1999), pages 35–62. Princeton Univ. Press, Princeton, NJ, 2002.  F. Diacu, E. P´erez-Chavela, and M. Santoprete. Central configurations and total collisions for quasihomogeneous n-body problems.
As a consequence, the usual analysis of collision and near collision motions can not be extended to this case. Example 6 (N –body potential reduced by a symmetry group satisfying the rotating circle property). The paper  deals with minimal trajectories to the spatial 2N –body problem under the hip–hop symmetry, where the configuration is constrained at all time to form a regular antiprism. This problem has three degrees of freedom and the reduced potential of a configuration generated by the point of coordinates (u, ζ) ∈ C × R R3 decomposes as K(N ) U (u, ζ) = + U0 (u, ζ), |u|α where K(N ) = N −1 1 , sinα ( kπ N ) k=1 N U0 (u, ζ) 1 = k=1 sin2 (2k−1)π 2N |u|2 + ζ 2 α 2 , The first term comes from the interaction among points of the same N –agon and is singular at simultaneous partial collisions on the ζ–axis.
Systems, 25(3):921–947, 2005.  P. Painlev´e. Le¸cons sur la th´eorie analytique des ´equations diff´erentielles. Hermann, Paris, 1897.  H. G. Saari. Singularities of the n-body problem. I. Arch. Rational Mech. , 30:263–269, 1968.  H. G. Saari. Singularities of the n-body problem. II. In Inequalities, II (Proc. S. , 1967), pages 255–259. Academic Press, New York, 1970.  H. Riahi. Study of the generalized solutions of n-body type problems with weak forces. , 28(1):49–59, 1997.  H.