caa a22 4500 477036988 CHVBK 20180405111307.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF02434056 doi (NATIONALLICENCE)springer-10.1007/BF02434056 Stewart I. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK aut Symmetry methods in collisionless many-body problems [Elektronische Daten] [I. Stewart] Summary: We formulate an appropriate symmetry context for studying periodic solutions to equal-mass many-body problems in the plane and 3-space. In a technically tractable but unphysical case (attractive force a smooth function of squared distance, bodies permitted to coincide) we apply the equivariant Moser-Weinstein Theorem of Montaldiet al. to prove the existence of various symmetry classes of solutions. In so doing we expoit the direct product structure of the symmetry group and use recent results of Dionneet al. on ‘C-axial' isotropy subgroups. Along the way we obtain a classification of C-axial subgroups of the symmetric group. The paper concludes with a speculative analysis of a three-dimensional solution to the 2n-body problem found by Davieset al. and some suggestion for further work. Springer-Verlag New York Inc, 1996 Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 543-563 0938-8974 6:6<543 1996 6 332 https://doi.org/10.1007/BF02434056 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02434056 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Stewart I. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/6(1996-11-01), 543-563 0938-8974 6:6<543 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer