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Monday 01 Dec 2014AG Dynamics seminar: Relative Lyapunov centre bifurcation

Claudia Wulff - University of Surrey

St John's room, Kay Building 16:00-17:00

Relative equilibria and relative periodic orbits (RPOs) are ubiquitous in symmetric mechanical systems and occur for example in celestial mechanics, molecular dynamics and rigid body motion. Relative equilibria are equilibria and RPOs are periodic orbits of the symmetry reduced system. A famous example of a relative equilibrium in celestial mechanics is the Lagrangian relative equilibrium of the N-body problem which is a rigidly rotating N-gon. A famous example of an RPO of the N-body problem is a rotating choreography where in a suitable corotating frame all bodies follow the same closed curve. Perturbation of a stable equiilbrium in a one degree of freedom mechanical system (say a pendulum) results in a periodic motion around the equilibrium. This is an example of a Lyapunov centre bifurcation. More generally, Lyapunov centre bifurcations are bifurcations of periodic orbits from equilibria in mechanical systems. Relative Lyapunov centre bifurcations are bifurcations of RPOs from relative equilibria corresponding to Lyapunov centre bifurcations of the symmetry reduced dynamics. In this talk we discuss relative Lyapunov centre bifurcations. and develop numerical methods for the detection and computation of relative Lyapunov centre bifurcations along branches of RPOs. We use our methods to study bifurcations of from Lagrangian relative equilibria in the N-body problem.

(Delivered by live video-link)

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