Abstract
We will show that for each k≠1, there exists an isolated singularity of a real analytic map from \(\mathbb {R}^{4}\) to \(\mathbb {R}^{2}\) which admits a real analytic deformation such that the set of singular values of the deformed map has a simple, innermost component with k outward cusps and no inward cusps. Conversely, such a singularity does not exist if k=1.
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