Abstract
Let M be a compact surface and let ā be the set of real numbers. When it is not specified explicitly, all the objects are supposed to be smooth (Cā- smooth).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Godbillon, C., 1983 Dynamical Systems on Surfaces,Springer.
GuttiĆ©rrez, C., 1975 Structural stability for line fields with singularities on two-dimensional manifolds,Lecture Notes in Math. 468, 17ā19, Springer.
GuttiĆ©rrez, C., 1988 Foliations on surfaces having exceptional leaves,Lecture Notes in Math. 1331, 73ā85, Springer.
Hector, G. and Hirsch, U., 1981 Introduction to the Geometry of Foliations, Part A and B,Vieweg & Sohn.
Imanishi, H., 1979 On codimension one foliations defined by closed one forms with singularities, J. Math. Kyoto Univ. 19ā2, 285ā291.
Kadyrov, A. A., 1983 Critical points of differential equations with unoriented trajectories in the plane, Differents. Uravn. 19, 2039ā2048, Translation: Differential Equations 19, 1473ā1483.
Katok, A. B., 1973 Invariant measures of flows on oriented surfaces, Soviet Math. Doklady 14, (4), 1104ā1108; DAN 211, No. 4, 775ā778.
Katok, A. and Hasselblatt, B., 1995 Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications, Cambridge Univ. Press.
Levitt, G., 1982 Pantalons et feuilletages des surfaces, Topology 21, 9ā33.
Moussu, R., 1970 Feuilletage sans holonomie dāune varietĆ© fermĆ©e, C.R. Acad. Sci. Paris 270, 1308ā1311.
Novikov, S. P., 1965 Topology of foliations, Trudy Mosk. Mat. Obshch. 14, 248ā278.
Tishler, D., 1970 On fibering certain foliated manifolds over S1, Topology 9, 153ā154.
Zorich, A., 1987 Quasiperiodic structure of the level surfaces of a Morse-Smale 1-form, close to rational. Problem of S. P. Novikov, Izv. Akad. Nauk SSSR 51, 1322ā1344.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
Ā© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nikolaev, I. (2001). Foliations on 2-Manifolds. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-04524-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08698-4
Online ISBN: 978-3-662-04524-4
eBook Packages: Springer Book Archive