Research
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.
- Patterns in convection, Faraday wave and Taylor-Couette experiments
- Secondary instabilities of patterns
- Mode interactions
- Hidden symmetries
- Quasipatterns and the small divisor problem
- Chaos in the presence of symmetry
- Cycling chaos
- Global bifurcations
- Synchronisation of coupled oscillators
- Takens-Bogdanov bifurcations
- Influence of magnetic fields on convection
- Structure and stability of flux tubes
- Formation of pores and sunspots
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