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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Completely unstable flows on $ 2$-manifolds


Author: Dean A. Neumann
Journal: Trans. Amer. Math. Soc. 225 (1977), 211-226
MSC: Primary 58F10
MathSciNet review: 0448440
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Abstract: Completely unstable flows on 2-manifolds are classified under both topological and $ {C^r}$-equivalence $ (1 \leqslant r \leqslant \infty )$, in terms of the corresponding orbit spaces.


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  • [1] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag, New York-Berlin, 1970. MR 0289890
  • [2] André Haefliger and Georges Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseignement Math. (2) 3 (1957), 107–125 (French). MR 0089412
  • [3] Otomar Hájek, Sections of dynamical systems in 𝐸², Czechoslovak Math. J. 15 (90) (1965), 205–211 (English, with Russian summary). MR 0176181
  • [4] Wilfred Kaplan, Regular curve-families filling the plane, I, Duke Math. J. 7 (1940), 154–185. MR 0004116
  • [5] Lawrence Markus, Parallel dynamical systems, Topology 8 (1969), 47–57. MR 0234489
  • [6] James Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. (2) 72 (1960), 521–554. MR 0121804
  • [7] Dean Neumann, Smoothing continuous flows, J. Differential Equations 24 (1977), no. 1, 127–135. MR 0431280
  • [8] T. Ważewski, Sur un problème de caractère intégral relatif à l'équation $ \partial z/\partial x + Q(x,y)\partial z/\partial y = 0$, Mathematica 8 (1934), 103-116.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0448440-0
Keywords: Flows on 2-manifolds, $ {C^r}$-equivalence of flows, orbit space
Article copyright: © Copyright 1977 American Mathematical Society