The Free Surface of a Magnetic Fluid.

Changes in the form of the free surface of a magnetic fluid under the influence of gravity, surface tension and a magnetic field are studied. A static infinite layer model for the phenomenon as a bifurcation problem on the hexagonal lattice is considered. By means of the Liapunov -Schmidt method the model is reduced to a bifurcation problem studied by Buzano and Golubitsky. Using these methods the transition from a flat surface to a hexagonal surface pattern observed in experiments is analyzed.