Steckles, Katrina
(2011)
*Loop Spaces and Choreographies in Dynamical Systems.*
Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## Abstract

We consider a subset of the set of solutions to the n-body problem, termed choreographies, which involve a motion of particles where each follows the same path in space with a fixed time delay. Focusing on planar choreographies, we use the action of symmetry groups on the spatial and temporal motion of such systems to restrict a space of loops and study the topology of the resulting manifolds. As well as providing a framework of notation and terminology for the study of such systems, we prove various useful properties which allow us to classify the possible groups of symmetries, and discuss which are likely to be realisable as that of a motion of bodies.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | N-body problems, Choreographies, Spatio-Temporal symmetry, Symmetric minimizers, Loop spaces |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology |

Depositing User: | Dr James Montaldi |

Date Deposited: | 24 Apr 2012 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1807 |

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