# Multiplicities of bifurcation sets of Pham singularities

## TL;DR

This paper calculates the local multiplicities of bifurcation sets in Pham singularities and related sets, providing insights into the complexity of algorithms for classifying real function singularities.

## Contribution

It introduces calculations of multiplicities for Maxwell and generalized Stokes' sets in Pham singularities, advancing understanding of bifurcation structures.

## Key findings

- Calculated local multiplicities for Maxwell sets in Pham singularities
- Extended calculations to generalized Stokes' sets with complex relations
- Discussed implications for algorithmic classification of real singularities

## Abstract

The local multiplicities of the Maxwell sets in the spaces of versal deformations of Pham holomorphic function singularities are calculated. A similar calculation for some other bifurcation sets (generalized Stokes' sets) defined by more complicated relations between the critical values is given. Aplications to the complexity of algorithms enumerating topologically distinct morsifications of complicated real function singularities are discussed.