Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

Sur le nombre de Łojasiewicz à l'infini d'un polynôme

Pierrette Cassou-NoguèsHa Huy Vui — 1995

Annales Polonici Mathematici

Résumé. Soit f un polynôme à deux indéterminées. On appelle nombre de Łojasiewicz à l'infini de f le nombre de Łojasiewicz à l'infini de son application gradient. Dans cet article nous montrons tout d'abord que l'on peut calculer le nombre de Łojasiewicz d'un polynôme à partir des diagrammes de Eisenbud et Neumann de toutes les courbes f(x,y) = t. Ensuite nous montrons que l'on peut définir un nombre de Łojasiewicz intrinsèque en prenant le maximum des nombres de Łojasiewicz de f ∘ ϕ si f est bon...

On the Łojasiewicz exponent at infinity of real polynomials

Ha Huy VuiPham Tien Son — 2008

Annales Polonici Mathematici

Let f: ℝⁿ → ℝ be a nonconstant polynomial function. Using the information from the "curve of tangency" of f, we provide a method to determine the Łojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Łojasiewicz exponent at infinity is finite or not. Then we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Łojasiewicz exponent at infinity of f and the problem of computing...

Łojasiewicz exponent of the gradient near the fiber

Ha Huy VuiNguyen Hong Duc — 2009

Annales Polonici Mathematici

It is well-known that if r is a rational number from [-1,0), then there is no polynomial f in two complex variables and a fiber f - 1 ( t ) such that r is the Łojasiewicz exponent of grad(f) near the fiber f - 1 ( t ) . We show that this does not remain true if we consider polynomials in real variables. More exactly, we give examples showing that any rational number can be the Łojasiewicz exponent near the fiber of the gradient of some polynomial in real variables. The second main result of the paper is the formula...

Page 1

Download Results (CSV)