My Research Papers
All papers here are in pdf format (unless otherwise stated)
-  Two body problem on a sphere in the presence of a uniform magnetic field.
-  Attracting and repelling 2-body problems on a family of surfaces of
-  Generalized point vortex dynamics on CP2.
-  Non-Abelian momentum polytopes for products of CP2.
-  Integrability and dynamics of the n-dimensional symmetric Veselova top.
-  Persistence of stationary motion under explicit symmetry breaking perturbation.
-  Hermitian flag manifolds and orbits of the Euclidean group.
-  Reduction and relative equilibria for the 2 body problem on spaces of constant curvature.
-  Feynman path integrals and Lebesgue-Feynman measures.
-  Gauge momenta as Casimir functions of nonholonomic systems.
-  Periodic orbits in Hamiltonian systems with involutory symmetries.
-  Transformations of Feynman path integrals and the generalized densities of Feynman pseudomeasures.
-  Hamiltonian relative equilibria with continuous isotropy/br>
(with Miguel Rodriguez-Olmos) [ArXiv]
-  Existence of symmetric central configurations.
-  Transformations of measures via their generalized densities.
-  Point vortices on the hyperbolic plane.
-  Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry.
-  Classification of symmetry groups for planar n-body choreographies.
-  A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy.
-  Deformation of geometry and bifurcations of vortex rings
-  Finite-dimensional behaviour and observability in a randomly forced PDE
(with Dave Broomhead, Jerry Huke, and Mark Muldoon) [mims eprint, DOI]
-  Generalized Dirichlet to Neumann operator on invariant differential forms and equivariant cohomology.
-  Witten-Hodge theory for manifolds with boundary and equivariant cohomology.
-  Point Vortices on the Sphere: Stability of Symmetric Relative Equilibria
(with Frédéric Laurent-Polz and Mark Roberts) [mims eprint, DOI] (new version)
-  Dynamics of poles with position-dependent strengths and its optical analogues.
-  On the stability of Hamiltonian relative equilibria with non-trivial isotropy.
-  Symplectic group actions and covering spaces
-  A note on the geometry of linear Hamiltonian systems
of signature 0 in R4
-  Stability of relative equilibria of point vortices on the sphere
(with Frédéric Laurent-Polz and Mark Roberts)
(new version above, )
-  Bifurcation and forced symmetry breaking in Hamiltonian systems.
-  The relation between local and global dual pairs.
-  Golden gaskets: variations on the Sierpinski sieve.
-  Relative periodic orbits of symmetric Lagrangian systems.
(with Chris McCord, Mark Roberts and Luca Sbano)
-  Vortex dynamics on cylinders.
(with Anik Soulière and Tadashi Tokieda)
-  Openness of momentum maps and persistence of extremal relative equilibria.
-  Group theoretic conditions for existence of robust relative homoclinic trajectories.
-  Relative equilibria of point vortices on the sphere.
(with Chjan Lim and Mark Roberts)
-  A note on semisymplectic actions of Lie groups.
-  Real continuation from the complex quadratic family: Fixed point bifurcation sets.
-  Perturbing a symmetric resonance: the magnetic spherical pendulum.
-  Relative equilibria of molecules.
-  Multiplicities of zero-schemes in quasi-homogeneous corank-1 singularities.
-  Persistance d'orbites périodiques relatives dans les systèmes hamiltoniens symétriques.
-  Persistence and stability of relative equilibria.
-  Bifurcation générique d'ondes rotatives d'isotropie maximale.
-  The path formulation of bifurcation theory.
-  Deformations of maps on complete intersections, Damon's KV-equivalence and bifurcations
(with David Mond) [Paper (222K)]
-  Multiplicities of critical points of invariant functions
-  Quotient spaces and critical points of invariant functions for C*-actions
-  On generic composites of mappings.
-  Caustics in time reversible Hamiltonian systems.
-  One-forms on singular curves and the topology of real curve singularities
(with Duco van Straten) [DOI]
-  Stability of nonlinear normal modes in symmetric Hamiltonian systems
-  Existence of nonlinear normal modes in symmetric Hamiltonian systems
-  Periodic solutions near equilibria of symmetric Hamiltonian systems
-  Non-linear normal modes of symmetric Hamiltonian systems
(with Mark Roberts and Ian Stewart) [Abstract]
-  Surfaces in 3-space and their contact with circles.
-  On contact between submanifolds.