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Equivariant normal forms via the Moser trick

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The Mathematics of Liquid Crystals

As is well known, phase transitions in Landau theory are described by bifurcations of critical points of the free energy. Phase transitions can be most easily analysed for certain normal forms, which contain a small number of essential terms. One would like to know when a given free energy can be brought into a normal form, locally at least, by a near-identity change of variables. If the free energy possesses some symmetries, then one would like this change of variables to preserve these symmetries.

Using as an example a free energy for biaxial nematic liquid crystals, I will discuss an approach to normal form transformations using Moser’s trick. The Moser trick reduces the nonlinear problem to a linear one through the determination of the generator of a one-parameter family of transformations linking the identity to the required transformation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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