Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T17:48:57.175Z Has data issue: false hasContentIssue false
  • English
  • Français

On the topological degree of real polynomial vector fields

Published online by Cambridge University Press:  18 May 2009

Zbigniew Szafraniec
Zbigniew Szafraniec
Affiliation:
University of Gdańsk, Institute of Mathematics, 80–952 Gdańsk, Wita Stwosza 57, Poland e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G: Rn → Rn be a continuous mapping such that the origin 0 ∈ Rn is isolated in G-1(0). Then deg0G will denote the local topological degree of G at the origin, i.e. the topological degree of the mapping

where Sr denotes a sphere in Rn centered at the origin with small radius r > 0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 2 , May 1996 , pp. 221 - 231
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Becker, E., Cardinal, J.-P., Roy, M.-F. and Szafraniec, Z., Multivariate Bezoutians, Kronecker symbol and Eisenbud-Levine formula, to appear in Proceedings of MEGA 94 Conference.Google Scholar
2.Bochnak, J., Coste, M. and Roy, M.-F., Géométrie algébrique réelle (Springer, 1987).Google Scholar
3.Coste, M., Ensembles semi-algébriques, Real algebraic geometry and quadratic forms (Rennes, 1981), Lecture Notes in Mathematics 959 (Springer, 1982), 109–138.Google Scholar
4.Coste, M., Sous-ensembles algébriques réels de codimension 2, Real analytic and algebraic geometry (Trento, 1988), Lecture Notes in Mathematics 1420 (Springer, 1990), 111–120.CrossRefGoogle Scholar
5.Coste, M. and Kurdyka, K., On the link of a stratum in a real algebraic set, Topology 31 (1992), 323–336.CrossRefGoogle Scholar
6.Dudziński, P., On topological invariants mod 2 of weighted homogeneous polynomials, to appear.Google Scholar
7.Dudziński, P., Ł¸ki, A., Nowak-Przygodzki, P. and Szafraniec, Z., On topological invariance of the Milnor number mod 2, Topology 32 (1993), 573–576. 007„ of the Milnor number mod 2, Topology 32 (1993), 573–576.Google Scholar
8.Fekak, A., Exposants de Łojasiewicz pour les fonctions semi-algébriques, Ann. Polon. Math. 56 (1992), 123–131.CrossRefGoogle Scholar
9.Hardt, R. M., Semi-algebraic local triviality in semi-algebraic mappings, Amer. J. Math. 102 (1980), 291–302.CrossRefGoogle Scholar
10.Hartman, P., Ordinary differential equations (Wiley, 1964).Google Scholar
11.Krasnosielski, M. A., Topological methods in the theory of nonlinear integral equations (Gosudarstv. Izdat. Tehn.-Teor. Lit., 1956).Google Scholar
12.Łojasiewicz, S., Ensembles semi-analytiques (IHES, 1965).Google Scholar
13.McCrory, C. and Parusiński, A., Complex monodromy and the topology of real algebraic sets, to appear.Google Scholar
14.Milnor, J. W., Singular points of complex hypersurfaces (Princeton University Press, 1968).Google Scholar
15.Nirenberg, L., Topics in nonlinear functional analysis (Courant Institute of Mathematical Sciences, New York University, 1974).Google Scholar
16.Szafraniec, Z., On the Euler characteristic of analytic and algebraic sets, Topology 25 (1986), 411–414.CrossRefGoogle Scholar
17.Szafraniec, Z., On the Euler characteristic mod 2 of real projective varieties, Math. Proc. Cambridge Philos. Soc. 104 (1988), 479–481.CrossRefGoogle Scholar
18.Szafraniec, Z., On the Euler characteristic mod 2 of real projective hypersurfaces, Bull. Polish Acad. Sci. Math. 37 (1989), 103–107.Google Scholar
19.Szafraniec, Z., Topological invariants of real analytic sets (Wydawnictwo Uniwersytetu Gdańskiego, 1993).Google Scholar
20.Varchenko, A. N., Theorems on the topological equisingularity of families of algebraic varieties and families of polynomial mappings, Izv. Akad. Nauk. SSSR Ser. Mat. 36 (1972), 957–1019.Google Scholar
21.Wall, C. T. C., Topological invariance of the Milnor number mod 2, Topology 22 (1983), 345–350.CrossRefGoogle Scholar
22.Wallace, A., Linear sections of algebraic varieties, Indiana Univ. Math. J. 20 (1970/1971), 1153–1162.CrossRefGoogle Scholar