Notes on trimodal singularities

Singularities of functions of modality 1 or 2 were classified by Arnold [3] . Types of those of modality 3 were listed in [14]. Here we show that these are all Newton nondegenerate in the extended sense introduced in [17], and use this fact to obtain explicit regular bases and precise normal forms fo r right and for contact equivalence. This requires care since the only exis ting method for non-semiquasihomogeneous germs (using Arnold's "Condition A ") does not apply to all our cases.