Symmetry Considerations

Non-linear evolution of a vector field

Symmetries constrain the evolution equations:

Full Rotation

Joint Rotation

• Linear equations with full rotation symmetry
• Linear equations with joint rotation symmetry

Nonlinear steady states [PNAS, 100, 16036 (2003)]

Full Rotation

Joint Rotation

Density of pin-wheels:

• Zeros of a random Gaussian field
• Evolution of the pinwheel density in the linear regime

Next Outline Previous Symmetries