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Classification of continuous flows on 2-manifolds
Author:
Dean A. Neumann
Journal:
Proc. Amer. Math. Soc. 48 (1975), 73-81
MathSciNet review:
0356138
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: We prove that a continuous flow with isolated critical points on an arbitrary  -manifold is determined up to topological equivalence by its separatrix configuration.
- [1]
N.
P. Bhatia and G.
P. Szegö, Stability theory of dynamical systems, Die
Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag,
New York, 1970. MR 0289890
(44 #7077)
- [2]
Otomar
Hájek, Sections of dynamical systems in
𝐸², Czechoslovak Math. J. 15 (90)
(1965), 205–211 (English, with Russian summary). MR 0176181
(31 #456)
- [3]
L.
Markus, Global structure of ordinary
differential equations in the plane, Trans.
Amer. Math. Soc. 76
(1954), 127–148. MR 0060657
(15,704a), http://dx.doi.org/10.1090/S0002-9947-1954-0060657-0
- [1]
- N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der math. Wissenschaften, Band 161, Springer-Verlag, New York and Berlin, 1970. MR 44 #7077. MR 0289890 (44:7077)
- [2]
- O. Hájek, Sections of dynamical systems in
 , Czechoslovak Math. J. 15 (90) (1965), 205-211. MR 31 #456. MR 0176181 (31:456)
- [3]
- L. Markus, Global structure of ordinary differential equations in the plane, Trans. Amer. Math. Soc. 76 (1954), 127-148. MR 15, 704. MR 0060657 (15:704a)
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1975-0356138-6
PII:
S 0002-9939(1975)0356138-6
Keywords:
Flows on  -manifolds,
separatrices
Article copyright:
© Copyright 1975 American Mathematical Society
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