Complutense University Library

Deformations of functions without real critical points

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

Official URL: http://www.tandfonline.com/doi/full/10.1081/AGB-120022790

View download statistics for this eprint

==>>> Export to other formats

Abstract

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).

Item Type:Article
Uncontrolled Keywords:Singularities; Real analytic function; One critical point; Deformation
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:16708
References:

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.

Deposited On:15 Oct 2012 08:09
Last Modified:15 Oct 2012 08:09

Repository Staff Only: item control page