Loop spaces and Choreographies in Dynamical Systems

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.

Date of Award	31 Dec 2011
Original language	English
Awarding Institution	The University of Manchester
Supervisor	James Montaldi (Supervisor) & Charles Walkden (Supervisor)