Geodesic
Logarithmic structure of the generalized bifurcation set
Annales Polonici Mathematici, Tome 63 (1996) no. 2, pp. 187-197 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ap-63-2-187-197
Keywords: bifurcations, singularities, logarithmic stratifications

S. Janeczko 1

1 
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S. Janeczko. Logarithmic structure of the generalized bifurcation set. Annales Polonici Mathematici, Tome 63 (1996) no. 2, pp. 187-197. doi: 10.4064/ap-63-2-187-197

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