Publication: The asymptotic values of a polynomial function on the real plane.
Loading...
Files
Full text at PDC
Publication Date
1996
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
Let a polynomial function f of two real variables be given. We prove the existence of a finite number of unbounded regions of the real plane along which the tangent planes to the graph of f tend to horizontal position, when moving away from the origin. The real limit values of this function on these regions are called asymptotic values. We also define the real critical values at infinity of f and prove the theorem of local trivial fibration at infinity, away from these values.
Description
UCM subjects
Unesco subjects
Keywords
Citation
J. Bochnak, M. Coste, M.F. Roy, Gtomdtrie algebrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3 Folge, Band 12 (Springer, Berlin, 1987).
N. Bourbaki, Elements of Mathematics, General Topology, part 1 (Addison-Wesley, Reading, Mass., 1966).
A. Durfee, N. Kronenfeld, H. Munson, J. Roy, I. Westby, Counting critical points of real polynomials in two variables, Amer. Math. Mon. 100(3), (1993), 255-271.
L. Fourrier, Entrelacs a l’infini et types topologiques des polynomes de deux variables complexes, These, University Paul Sabatier de Toulouse, 1993.
H.V. Ha, Sur la fibration globale des polynbmes de deux variables complexes, C.R. Acad. Sci. Paris 309, serie I (1989) 231-234.
H.V. Ha, Nombres de Lojasiewicz et singularitis a l’infini des polynbmes de deux variables complexes, C.R. Acad. Sci. Paris 311, serie I (1990) 429-432.
H.V. Ha, D.T. Lt, Sur la topologie des polynomes complexes, Acta Math. Viet., 9(l) (1984) 21-32.
H.V. Ha, L.A. Nguyen, Le comportement geomitrique a l’infini des polynbmes de deux variables complexes, C.R. Acad. Sci. Paris 309, serie I (1989) 183-186.
S. Pinchuk, A counterexample to the strong real Jacobian conjecture, Math. Z. 217 (1994) 1-4.
M. Shiota, Nash Manifolds, Lecture Notes in Mathematics, Vol. 1267, (Springer, Berlin, 1980).