Logarithmic structure of the generalized bifurcation set

S. Janeczko¹

¹

Annales Polonici Mathematici, Tome 63 (1996) no. 2, pp. 187-197.

Résumé

Let $G: ℂ^{n} × ℂ^{r} → ℂ$ be a holomorphic family of functions. If $Λ ⊂ ℂ^{n} × ℂ^{r}$, $π_r: ℂ^{n} × ℂ^{r} → ℂ^{r}$ is an analytic variety then   $Q_{Λ}(G) = {(x,u) ∈ ℂ^{n} × ℂ^{r}: G(·,u)$ has a critical point in $Λ ∩ π_{r}^{-1}(u)} is a natural generalization of the bifurcation variety of G. We investigate the local structure of $Q_{Λ}(G)$ for locally trivial deformations of $Λ₀ = π_{r}^{-1}(0)$. In particular, we construct an algorithm for determining logarithmic stratifications provided G is versal.

Détail

DOI : 10.4064/ap-63-2-187-197

Keywords: bifurcations, singularities, logarithmic stratifications