Biblioteca de la Universidad Complutense de Madrid

Deformations of functions without real critical points


Luengo Velasco, Ignacio y González Ramírez, Jorge A. (2003) Deformations of functions without real critical points. Communications in Algebra, 31 (9). pp. 4255-4266. ISSN 0092-7872

URL Oficial:


Given a real analytic function f(x, y) with one critical point P-0, we Study deformations f(1) of f such that, for any t not equal 0, the analytic function f(t) has no critical points in a neighborhood of P-0. We give explicitly a deformation without real critical points for any function which has only one real branch with characteristic exponents (4, 2q, r).

Tipo de documento:Artículo
Palabras clave:Singularities; Real analytic function; One critical point; Deformation
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:16708

A'Campo, N. (1975). Le groupe de monodromie du déploiment des singularites isolées de courbes planes I. Math. Ann. 213, Springer-Verlag, pp. 1–32.

Arnold, V. I. (1978). Index of a singular point of a vector field, the petrovskii-oleinik inequality, and mixed hodge structures. Functional Analysis and its Applications 12:1–11.

Brieskorn, E., Knorrer, H. (1986). Plane Algebraic Curves. Basel: Birkhauser-Verlag.

Campillo, A. (1980). Algebroid Curves in Positive Characteristic. Vol. 813. Lecture Notes in Math., Berlin-Heidelberg-New York: Springer-Verlag.

González-Ramírez, J. A. (1996). Contribución al estudio de las deformaciones de singularidades reales, Ph.D. thesis, Universidad Nacional de Educación a Distancia.

Gusein-Zade, S. M.: Dynkin diagrams for singularities of functions of two variables, Funktsionalnyi Analiz i ego Prilozheniya 8/4, pp. 23–30. (engl. Übers. in Functional Analysis and its Applications), 1974.

Gusein-Zade, S. M. (1997). On the existence of deformations without critical points (The Teissier problem for functions of two variables). Funct. Anal. Appl. 31(1):58–60.

Luengo, I., Pfister, G. (1990). Normal forms and moduli spaces of curve singularities with semigroup (2p,2q,2pq+d). Comp. Math. 76:247–264.

Milnor, J. (1965). Topology from the Differentiable Viewpoint. Charlottesville: The University Press of Virginia.

Teissier, B. (1983). Appendix: on tree questions of finiteness in real analytic geometry. Acta Math. 151(1–2):39–48.

Depositado:15 Oct 2012 08:09
Última Modificación:15 Oct 2012 08:09

Sólo personal del repositorio: página de control del artículo