My main research activities can be divided into three areas: analysis of chaotic dynamics in nonlinear differential equations, usually in the presence of symmetry; pattern formation in fluid dynamics and more general problems; and the application of these ideas to problems in astrophysical fluid dynamics, in particular, to solar physics: convection in the Sun and how it is influenced by magnetic field, in particular in sunspots.

Pattern formation

  • Patterns in convection, Faraday wave and Taylor-Couette experiments
  • Secondary instabilities of patterns
  • Mode interactions
  • Hidden symmetries
  • Quasipatterns and the small divisor problem

Nonlinear dynamics

  • Chaos in the presence of symmetry
  • Cycling chaos
  • Global bifurcations
  • Synchronisation of coupled oscillators
  • Takens-Bogdanov bifurcations

Astrophysical fluid dynamics and magnetohydrodynamics

  • Influence of magnetic fields on convection
  • Structure and stability of flux tubes
  • Formation of pores and sunspots