The asymptotic values of a polynomial function on the real plane.
| dc.contributor.author | Ferrera Cuesta, Juan | |
| dc.contributor.author | Puente Muñoz, María Jesús De La | |
| dc.date.accessioned | 2023-06-20T16:51:34Z | |
| dc.date.available | 2023-06-20T16:51:34Z | |
| dc.date.issued | 1996 | |
| dc.description.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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | D.G.I.C.Y.T. | |
| dc.description.sponsorship | C.I.C.Y.T. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15289 | |
| dc.identifier.doi | 10.1016/0022-4049(95)00025-9 | |
| dc.identifier.issn | 0022-4049 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/0022404995000259 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57251 | |
| dc.issue.number | 3 | |
| dc.journal.title | Journal of Pure and Applied Algebra | |
| dc.language.iso | eng | |
| dc.page.final | 273 | |
| dc.page.initial | 263 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PB 90/0044. | |
| dc.relation.projectID | PB 89/0379-CO2-02. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986.6 | |
| dc.subject.cdu | 517.518.45 | |
| dc.subject.keyword | Complex-Variables | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | The asymptotic values of a polynomial function on the real plane. | |
| dc.type | journal article | |
| dc.volume.number | 106 | |
| dcterms.references | 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). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 | |
| relation.isAuthorOfPublication | 630e203d-3f7d-46d6-a43c-cb07da8c4b71 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 |
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