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Talk Abstract
Bifurcations of Periodic Orbits with Spatio-Temporal Symmetries

Institute for Mathematics and Its Applications
Alastair Rucklidge, University of Cambridge

Motivated by recent analytical and numerical work on two- and three-dimensional convection with imposed spatial periodicity, we analyse examples of bifurcations from a continuous group orbit of spatio-temporally symmetric periodic solutions of partial differential equations. The presence of spatial symmetries can lead to a doubling of the marginal Floquet multiplier and to bifurcation to drifting patterns. We propose a systematic way of analysing bifurcations of periodic orbits with discrete spatio-temporal symmetries, which is relevant to other pattern formation problems, and contributes to our understanding of the transition from ordered to disordered behaviour in pattern-forming systems.

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