Keywords
- Vector Field
- Singular Point
- Newton Polyhedron
- Algebraic Manifold
- Smooth Vector Field
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arnol'd V.I., The index of a vector field singular point, Petrovsky-Oleinik inequalities, and Hodge's mixed structures. Funkts. analiz i ego prilozh., 1978, v. 12, No. 1, p. 1–14 (in Russian).
Arnol'd V.I., Additional chapters in the theory of ordinary differential equations. Moscow, Nauka, 1978 (in Russian).
Arnol'd V.I. and Oleinik O.A., The topology of real-valued algebraic manifolds. Vestnik MGU. Ser.1, Matem. i Mekh., 1979, No. 6, p. 7–17 (in Russian).
Berezovskaya F.S., Complicated stationary point of a system on a plane: neighbourhood structure and index. Pushchino, 1978. Preprint-Research centre for biological studies and Research computing centre of the USSR Academy of Sciences (in Russian).
Berezovskaya F.S., The index of stationary point of a vector field on a plane. Funkts. analiz i ego prilozh., 1979, v. 13, No. 2, p. 77 (in Russian).
Bershtein D.N., The number of roots of a system of equations. Funkts. analiz i ego prilozh., 1975, v. 9, No. 3, p. 1–4 (in Russian).
Bershtein D.N., Kushnirenko A.G., and Khovansky A.G., Newton polyhedrons. Usp. Matem. Nauk, 1976, v. 31, No. 3, p. 201–202 (in Russian).
Bliznyakov N.M., On rotation estimates for vector fields on algebraic manifolds. Funkts. analiz i ego prilozh., 1979, v. 13, No. 2, p. 78 (in Russian).
Bliznyakov N.M., On topological index estimates for a singular point of a vector field. Deposited at VINITI, 1979, No. 589-79 (in Russian).
Bliznyakov N.M., Calculation and estimates of a vector field singular point on a plane. Deposited at VINITI, 1979, No. 3041-79 (in Russian).
Bliznyakov N.M., Cauchy indices and singular point index of a vector field. In: Application of topology in modern analysis. Voronezh State University, 1985, p. 3–21 (in Russian).
Bliznyakov N.M. and Mukhamadiev E.M., On the calculation of singular point index for a polylinear vector field. Trudy Matem. Fak. VGU, 1971, No. 4, p. 19–29 (in Russian).
Busemann H., Convex surfaces. Interscience, New York
Gantmakher F.R., Matrix theory. Moscow, Nauka, 1967 (in Russian).
Krasnosel'sky M.A., Vainiko G.M., Zabreiko P.P., Rutitsky Ya.B., and Stetsenko V.Ya., Approximate solution of operator equations. Moscow, Nauka, 1969 (in Russian).
Kushnirenko A.G., Newton polyhedron and the number of solutions for a system of k equations with k unknown variables. Usp. Matem. Nauk, 1975, v. 30, No. 2, p. 266–267 (in Russian).
Postnikov M.M., Stable polynomials. Moscow, Nauka, 1981 (in Russian).
Khovansky A.G., The index of a polynomial vector field. Funkts. analiz i ego prilozh., 1979, v. 13, No. 1, p. 49–58 (in Russian).
Khovansky A.G., On a certain class of systems of transcendental equations. Doklady AN SSSR, 1980, v. 255, No.4, p.804–807 (in Russian).
Khovansky A.G. Newton polyhedrons and the index of a vector field. Usp. Matem. Nauk, 1981, v. 36, No. 4, p. 234 (in Russian).
Eisenbud D. and Levine H., An algebraic formula for the degree of a C map germ. Ann. Math., 1977, v. 106, No. 1, p. 19–44.
Granger M., Sur le degré local d'un germe d'application analytique réele. Comptes Rendus Acad. Sci. Paris. Sér. A et B, 1978, v. 287, No. 7, p. 531–534.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this chapter
Cite this chapter
Bliznyakov, N.M. (1988). Topological index estimates. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A. (eds) Global Analysis — Studies and Applications III. Lecture Notes in Mathematics, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080429
Download citation
DOI: https://doi.org/10.1007/BFb0080429
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50019-3
Online ISBN: 978-3-540-45894-4
eBook Packages: Springer Book Archive
