2013.26: Classification of symmetry groups for planar n-body choreographies
2013.26: James Montaldi and Katrina Steckles (2013) Classification of symmetry groups for planar n-body choreographies.
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Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part we classify all possible symmetry groups of planar n-body, collision-free choreographies. These symmetry groups fall in to 2 infinite families and, if n is odd, three exceptional groups. In the second part we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||Equivariant dynamics, n-body problem, variational problems, loop space, equivariant topology, braid group|
|Subjects:||MSC 2000 > 37 Dynamical systems and ergodic theory|
MSC 2000 > 58 Global analysis, analysis on manifolds
MSC 2000 > 70 Mechanics of particles and systems
|Deposited By:||Dr James Montaldi|
|Deposited On:||22 May 2013|
Available Versions of this Item
- Classification of symmetry groups for planar n-body choreographies (deposited 14 November 2013)
- Classification of symmetry groups for planar n-body choreographies (deposited 22 May 2013) [Currently Displayed]