PhD studentship: Bifurcations in symmetric Hamiltonian systems

University of Surrey

Supervisor name: Dr Claudia Wulff

Funding status: Competition Funded Project (Students Worldwide)

Project description: Relative equilibria (REs) 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. An example of an RE is a rigid body submersed in an ideal fluid that rotates around its axis and travels at constant speed. A perturbation away from a stable RE can lead to oscillations in a co-moving frame which correspond to RPOs. This is an example of a bifurcation. In this project a general theory for bifurcations of REs and RPOs will be developed for Hamiltonian systems with symmetry. The emphasis will be on systems with non-compact, non-abelian symmetry groups, such as the Euclidean group of rotations and translations in space – the symmetry group of the Kirchhoff model for a rigid body in an ideal fluid. We will also incorporate time-reversing symmetries. We will in particular study persistence of REs and RPOs to nearby level sets of the conserved quantities of the system, such as energy, angular and linear momentum, extending existing theories, and will investigate the relationship between persistence and stability of REs.

The project requires knowledge (or an eagerness to acquire knowledge) in the fields of Lagrangian and Hamiltonian systems, dynamical systems, Lie group theory and basic differential geometry.

Funding notes: The Faculty has a number of fully funded PhD studentships for UK and EU nationals who can demonstrate the appropriate residency requirements. These studentships will include the tuition fees and a tax-free stipend. The Department has also a few scholarships for partial funding for overseas fees. However, funding for overseas students is limited and overseas students are encouraged to find suitable funding themselves.

Application enquiries: Dr Matt Turner

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South East England