Phase transitions with several order parameters

The predictions of catastrophe theory for phase transitions involving more than one order parameter are given. These predictions are compared with those of other theories. For the simplest transition involving two order parameters it is found that there is a parameter which does not affect the topology of the phase diagram, which does affect certain angles in the diagram, and whose measured value will not depend on the scale of external physical variables. Comparison with renormalization theory predictions for this parameter leads to general observations on the relation of catastrophe theory and renormalization theory.